From f6689bb681d6b7d0e7a8fa0ead72ba92acb0a991 Mon Sep 17 00:00:00 2001 From: domi41 Date: Tue, 25 Mar 2025 15:21:44 +0100 Subject: [PATCH 01/19] feat: compute merit for proportional representation MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Thanks Marc Paraire for the neat idea for a meaningful score ! "Si tu ne te plantes pas tu ne pousseras jamais." — Copeau --- .../mj/MajorityJudgmentDeliberator.java | 58 +++++- .../java/fr/mieuxvoter/mj/ProposalResult.java | 32 +++ .../mj/ProposalResultInterface.java | 6 + .../mieuxvoter/mj/ProposalTallyAnalysis.java | 3 +- .../mj/MajorityJudgmentDeliberatorTest.java | 195 +++++++++++++++++- 5 files changed, 286 insertions(+), 8 deletions(-) diff --git a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java index 47b75b5..81ecb35 100644 --- a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java +++ b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java @@ -42,6 +42,7 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep BigInteger amountOfJudges = tally.getAmountOfJudges(); Integer amountOfProposals = tally.getAmountOfProposals(); + BigInteger sumOfMerits = BigInteger.ZERO; Result result = new Result(); ProposalResult[] proposalResults = new ProposalResult[amountOfProposals]; @@ -49,12 +50,15 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep for (int proposalIndex = 0; proposalIndex < amountOfProposals; proposalIndex++) { ProposalTallyInterface proposalTally = tallies[proposalIndex]; String score = computeScore(proposalTally, amountOfJudges); + BigInteger merit = computeMerit(proposalTally, amountOfJudges, this.favorContestation); + sumOfMerits = sumOfMerits.add(merit); ProposalTallyAnalysis analysis = new ProposalTallyAnalysis( proposalTally, this.favorContestation ); ProposalResult proposalResult = new ProposalResult(); proposalResult.setIndex(proposalIndex); proposalResult.setScore(score); + proposalResult.setMerit(merit); proposalResult.setAnalysis(analysis); // proposalResult.setRank(???); // rank is computed below, AFTER the score pass proposalResults[proposalIndex] = proposalResult; @@ -66,7 +70,7 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep proposalResultsSorted, (Comparator) (p0, p1) -> p1.getScore().compareTo(p0.getScore())); - // III. Attribute a rank to each Proposal + // III. Attribute a rank to each Proposal and compute their merit int rank = 1; for (int proposalIndex = 0; proposalIndex < amountOfProposals; proposalIndex++) { ProposalResult proposalResult = proposalResultsSorted[proposalIndex]; @@ -79,6 +83,8 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep } proposalResult.setRank(actualRank); rank += 1; + + proposalResult.computeMeritAsPercentage(sumOfMerits); } result.setProposalResults(proposalResults); @@ -126,7 +132,7 @@ private boolean isTallyBalanced(TallyInterface tally) { } /** - * @see computeScore() below + * @see this#computeScore(ProposalTallyInterface, BigInteger, Boolean, Boolean) below */ private String computeScore(ProposalTallyInterface tally, BigInteger amountOfJudges) { return computeScore(tally, amountOfJudges, this.favorContestation, this.numerizeScore); @@ -134,7 +140,7 @@ private String computeScore(ProposalTallyInterface tally, BigInteger amountOfJud /** * A higher score means a better rank. Assumes that grades' tallies are provided from "worst" - * grade to "best" grade. + * grade to "best" grade. This score is fast to compute but is not meaningful. * * @param tally Holds the tallies of each Grade for a single Proposal * @param amountOfJudges Amount of judges participating @@ -193,6 +199,52 @@ private String computeScore( return score.toString(); } + private BigInteger computeMerit( + ProposalTallyInterface tally, + BigInteger amountOfJudges, + Boolean favorContestation + ) { + ProposalTallyAnalysis analysis = new ProposalTallyAnalysis(); + analysis.reanalyze(tally, favorContestation); + + int amountOfGrades = tally.getTally().length; + + ProposalTallyInterface currentTally = tally.duplicate(); + + BigInteger merit = BigInteger.valueOf(analysis.getMedianGrade()); + Integer cursorGrade = analysis.getMedianGrade(); + Integer minProcessedGrade = cursorGrade; + Integer maxProcessedGrade = cursorGrade; + + for (int i = 0; i < amountOfGrades - 1; i++) { + + merit = merit.multiply(amountOfJudges); + + if (analysis.getSecondMedianGroupSize().compareTo(BigInteger.ZERO) == 0) { + continue; + } + + if (analysis.getSecondMedianGroupSign() > 0) { + cursorGrade = maxProcessedGrade + 1; + maxProcessedGrade = cursorGrade; + } else { + cursorGrade = minProcessedGrade - 1; + minProcessedGrade = cursorGrade; + } + + merit = merit.add( + analysis.getSecondMedianGroupSize().multiply( + BigInteger.valueOf(analysis.getSecondMedianGroupSign()) + ) + ); + + currentTally.moveJudgments(analysis.getMedianGrade(), cursorGrade); + analysis.reanalyze(currentTally, favorContestation); + } + + return merit; + } + private int countDigits(int number) { return ("" + number).length(); } diff --git a/src/main/java/fr/mieuxvoter/mj/ProposalResult.java b/src/main/java/fr/mieuxvoter/mj/ProposalResult.java index 4c44f06..e1eade7 100644 --- a/src/main/java/fr/mieuxvoter/mj/ProposalResult.java +++ b/src/main/java/fr/mieuxvoter/mj/ProposalResult.java @@ -1,5 +1,9 @@ package fr.mieuxvoter.mj; +import java.math.BigInteger; + +import static java.lang.Math.round; + public class ProposalResult implements ProposalResultInterface { protected Integer index; @@ -8,6 +12,10 @@ public class ProposalResult implements ProposalResultInterface { protected String score; + protected BigInteger merit = BigInteger.ZERO; + + protected Double meritAsPercentage = 0.0; + protected ProposalTallyAnalysis analysis; public Integer getIndex() { @@ -34,6 +42,30 @@ public void setScore(String score) { this.score = score; } + public BigInteger getMerit() { + return merit; + } + + public void setMerit(BigInteger merit) { + this.merit = merit; + } + + public Double getMeritAsPercentage() { + return meritAsPercentage; + } + + public void computeMeritAsPercentage(BigInteger sumOfMerits) { + if (sumOfMerits.compareTo(BigInteger.ZERO) == 0) { + this.meritAsPercentage = 0.0; + return; + } + + long precision = 1_000_000_000; // big enough for 7 billion humans + this.meritAsPercentage = round(this.getMerit().multiply( + BigInteger.valueOf(100 * precision * 10) + ).divide(sumOfMerits).doubleValue() / 10.0) / (double) precision; + } + public ProposalTallyAnalysis getAnalysis() { return analysis; } diff --git a/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java b/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java index 8a666d6..b821b4e 100644 --- a/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java +++ b/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java @@ -1,5 +1,7 @@ package fr.mieuxvoter.mj; +import java.math.BigInteger; + public interface ProposalResultInterface { /** @@ -23,6 +25,10 @@ public interface ProposalResultInterface { */ String getScore(); + BigInteger getMerit(); + + Double getMeritAsPercentage(); + /** Get more data about the proposal tally, such as the median grade. */ ProposalTallyAnalysis getAnalysis(); } diff --git a/src/main/java/fr/mieuxvoter/mj/ProposalTallyAnalysis.java b/src/main/java/fr/mieuxvoter/mj/ProposalTallyAnalysis.java index e1c49e0..0f23956 100644 --- a/src/main/java/fr/mieuxvoter/mj/ProposalTallyAnalysis.java +++ b/src/main/java/fr/mieuxvoter/mj/ProposalTallyAnalysis.java @@ -10,7 +10,8 @@ *

This uses BigInteger because in a normalization scenario we use the smallest common multiple * of the amounts of judges of proposals. It makes the code harder to read and understand, but it * allows us to bypass the floating-point nightmare of the normalization of merit profiles, which is - * one way to handle default grades on some polls. + * one way to handle default grades on some polls. BigInteger is also used to compute the proportional + * score, a meaningful score for proportional representation, holding the merit of each proposal. */ public class ProposalTallyAnalysis { diff --git a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java index b5a505e..d78146f 100644 --- a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java +++ b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java @@ -10,11 +10,15 @@ import org.junit.jupiter.params.ParameterizedTest; import java.math.BigInteger; +import java.util.ArrayList; +import java.util.List; +import java.util.Arrays; import javax.json.JsonArray; import javax.json.JsonObject; import javax.json.JsonValue; + class MajorityJudgmentDeliberatorTest { @DisplayName("Test majority judgment deliberation from JSON assertions") @@ -100,14 +104,14 @@ void testDemoUsageWithBigNumbers() throws Throwable { new ProposalTallyInterface[]{ new ProposalTally( new Long[]{ - 11312415004L, 21153652410L, - 24101523299L, 18758623562L + 11_312_415_004L, 21_153_652_410L, + 24_101_523_299L, 18_758_623_562L } ), new ProposalTally( new Long[]{ - 11312415004L, 21153652400L, - 24101523299L, 18758623572L + 11_312_415_004L, 21_153_652_400L, + 24_101_523_299L, 18_758_623_572L } ), }); @@ -117,6 +121,57 @@ void testDemoUsageWithBigNumbers() throws Throwable { assertEquals(2, result.getProposalResults().length); assertEquals(2, result.getProposalResults()[0].getRank()); assertEquals(1, result.getProposalResults()[1].getRank()); + assertEquals("670593969998983161296550287442546", result.getProposalResults()[0].getMerit().toString()); + assertEquals("670593970055723546867335687341546", result.getProposalResults()[1].getMerit().toString()); + assertEquals(49.999999998, result.getProposalResults()[0].getMeritAsPercentage()); + assertEquals(50.000000002, result.getProposalResults()[1].getMeritAsPercentage()); + } + + @Test + @DisplayName("Test 7 billions humans") + void testSevenBillionHumans() throws Throwable { + DeliberatorInterface mj = new MajorityJudgmentDeliberator(); + TallyInterface tally = + new Tally( + new ProposalTallyInterface[]{ + new ProposalTally( + new Long[]{ + 1_000_000_000L, 1_000_000_000L, + 1_000_000_000L, 1_000_000_000L, + 1_000_000_000L, 1_000_000_000L, + 1_000_000_000L, + } + ), + new ProposalTally( + new Long[]{ + 7_000_000_000L, + 0L, 0L, 0L, 0L, 0L, 0L, + } + ), + new ProposalTally( + new Long[]{ + 0L, 0L, 0L, + 7_000_000_000L, + 0L, 0L, 0L, + } + ), + new ProposalTally( + new Long[]{ + 0L, 0L, 0L, 0L, 0L, 0L, + 7_000_000_000L + } + ), + }); + ResultInterface result = mj.deliberate(tally); + + assertEquals("302526000007202999999314000000097999999993000000001000000000", result.getProposalResults()[0].getMerit().toString()); + assertEquals("0", result.getProposalResults()[1].getMerit().toString()); + assertEquals("352947000000000000000000000000000000000000000000000000000000", result.getProposalResults()[2].getMerit().toString()); + assertEquals("705894000000000000000000000000000000000000000000000000000000", result.getProposalResults()[3].getMerit().toString()); + assertEquals(22.222222223, result.getProposalResults()[0].getMeritAsPercentage()); + assertEquals(0.0, result.getProposalResults()[1].getMeritAsPercentage()); + assertEquals(25.925925926, result.getProposalResults()[2].getMeritAsPercentage()); + assertEquals(51.851851852, result.getProposalResults()[3].getMeritAsPercentage()); } @Test @@ -387,6 +442,138 @@ void testNumericScore() throws Exception { assertEquals("104203003", result.getProposalResults()[1].getScore()); } + + @Test + @DisplayName("Test numeric merit") + void testNumericMerit() throws Throwable { + Integer amountOfJudges = 23; + DeliberatorInterface mj = new MajorityJudgmentDeliberator(); + TallyInterface tally = ( + new Tally( + new ProposalTallyInterface[]{ + new ProposalTally(new Integer[]{5, 2, 4, 2, 4, 1, 5}), + new ProposalTally(new Integer[]{3, 2, 7, 0, 4, 5, 2}), + new ProposalTally(new Integer[]{6, 5, 3, 0, 5, 1, 3}), + new ProposalTally(new Integer[]{2, 2, 4, 4, 5, 2, 4}), + }, + amountOfJudges + ) + ); + + ResultInterface result = mj.deliberate(tally); + + assertNotNull(result); + assertEquals("376024199", result.getProposalResults()[0].getMerit().toString()); + assertEquals("370032259", result.getProposalResults()[1].getMerit().toString()); + assertEquals("227896998", result.getProposalResults()[2].getMerit().toString()); + assertEquals("512739688", result.getProposalResults()[3].getMerit().toString()); + + assertEquals(25.292657097, result.getProposalResults()[0].getMeritAsPercentage()); + assertEquals(24.889618984, result.getProposalResults()[1].getMeritAsPercentage()); + assertEquals(15.329121475, result.getProposalResults()[2].getMeritAsPercentage()); + assertEquals(34.488602444, result.getProposalResults()[3].getMeritAsPercentage()); + + assertEquals(100.0, + result.getProposalResults()[0].getMeritAsPercentage() + + result.getProposalResults()[1].getMeritAsPercentage() + + result.getProposalResults()[2].getMeritAsPercentage() + + result.getProposalResults()[3].getMeritAsPercentage() + ); + } + + @Test + @DisplayName("Generate merit distribution") + void testMeritDistribution() throws Throwable { + + class ProposalTallyFactory { + + private final Integer amountOfGrades; + private final Integer amountOfJudges; + + public ProposalTallyFactory( + Integer amountOfGrades, + Integer amountOfJudges + ) { + this.amountOfGrades = amountOfGrades; + this.amountOfJudges = amountOfJudges; + } + + public ProposalTallyInterface[] generateAll() { + ArrayList all = new ArrayList<>(); + + List tallies = multichoose(amountOfGrades, amountOfJudges); + for (Integer[] t : tallies) { + all.add(new ProposalTally(t)); + } + + return all.toArray(new ProposalTally[0]); + } + + /** + * All the ways to distribute k balls into n boxes. + * @param n amount of boxes + * @param k amount of balls + */ + private List multichoose(Integer n, Integer k) { + assert n >= 0; + assert k >= 0; + + ArrayList out = new ArrayList<>(); + + if (k == 0) { + ArrayList set = new ArrayList<>(); + for (int i = 0; i < n; i++) { + set.add(0); + } + out.add(set.toArray(new Integer[0])); + return out; + } + + if (n == 0) { + return out; + } + + if (n == 1) { + ArrayList set = new ArrayList<>(); + set.add(k); + out.add(set.toArray(new Integer[0])); + return out; + } + + for (Integer[] set: multichoose(n-1, k)) { + ArrayList seth = new ArrayList<>(); + seth.add(0); + seth.addAll(Arrays.asList(set)); + out.add(seth.toArray(new Integer[0])); + } + + for (Integer[] set: multichoose(n, k-1)) { + ArrayList seth = new ArrayList<>(); + + seth.add(set[0] + 1); + seth.addAll(Arrays.asList(Arrays.copyOfRange(set, 1, set.length))); + out.add(seth.toArray(new Integer[0])); + } + + return out; + } + } + + ProposalTallyFactory factory = new ProposalTallyFactory(5, 23); + DeliberatorInterface mj = new MajorityJudgmentDeliberator(); + TallyInterface tally = ( + new Tally( + factory.generateAll() + ) + ); + + ResultInterface result = mj.deliberate(tally); + + for (ProposalResultInterface proposalResult: result.getProposalResultsRanked()) { + System.out.print(proposalResult.getMerit().toString() + "\n"); + } + } + @Test @DisplayName("Fail on unbalanced tallies") void testFailureOnUnbalancedTallies() { From 1948cbd57333aaf5e3377bbd999b1e6cd2147047 Mon Sep 17 00:00:00 2001 From: domi41 Date: Wed, 26 Mar 2025 17:13:15 +0100 Subject: [PATCH 02/19] refacto: extract the proposal tally factory --- .../mj/MajorityJudgmentDeliberatorTest.java | 117 +++++------------- .../mieuxvoter/mj/ProposalTallyFactory.java | 87 +++++++++++++ 2 files changed, 117 insertions(+), 87 deletions(-) create mode 100644 src/test/java/fr/mieuxvoter/mj/ProposalTallyFactory.java diff --git a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java index d78146f..6ba4cb3 100644 --- a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java +++ b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java @@ -475,103 +475,46 @@ void testNumericMerit() throws Throwable { assertEquals(100.0, result.getProposalResults()[0].getMeritAsPercentage() - + result.getProposalResults()[1].getMeritAsPercentage() - + result.getProposalResults()[2].getMeritAsPercentage() - + result.getProposalResults()[3].getMeritAsPercentage() + + result.getProposalResults()[1].getMeritAsPercentage() + + result.getProposalResults()[2].getMeritAsPercentage() + + result.getProposalResults()[3].getMeritAsPercentage() ); } @Test - @DisplayName("Generate merit distribution") + @DisplayName("Generate merit distribution CSV") void testMeritDistribution() throws Throwable { - - class ProposalTallyFactory { - - private final Integer amountOfGrades; - private final Integer amountOfJudges; - - public ProposalTallyFactory( - Integer amountOfGrades, - Integer amountOfJudges - ) { - this.amountOfGrades = amountOfGrades; - this.amountOfJudges = amountOfJudges; - } - - public ProposalTallyInterface[] generateAll() { - ArrayList all = new ArrayList<>(); - - List tallies = multichoose(amountOfGrades, amountOfJudges); - for (Integer[] t : tallies) { - all.add(new ProposalTally(t)); - } - - return all.toArray(new ProposalTally[0]); - } - - /** - * All the ways to distribute k balls into n boxes. - * @param n amount of boxes - * @param k amount of balls - */ - private List multichoose(Integer n, Integer k) { - assert n >= 0; - assert k >= 0; - - ArrayList out = new ArrayList<>(); - - if (k == 0) { - ArrayList set = new ArrayList<>(); - for (int i = 0; i < n; i++) { - set.add(0); - } - out.add(set.toArray(new Integer[0])); - return out; - } - - if (n == 0) { - return out; - } - - if (n == 1) { - ArrayList set = new ArrayList<>(); - set.add(k); - out.add(set.toArray(new Integer[0])); - return out; - } - - for (Integer[] set: multichoose(n-1, k)) { - ArrayList seth = new ArrayList<>(); - seth.add(0); - seth.addAll(Arrays.asList(set)); - out.add(seth.toArray(new Integer[0])); - } - - for (Integer[] set: multichoose(n, k-1)) { - ArrayList seth = new ArrayList<>(); - - seth.add(set[0] + 1); - seth.addAll(Arrays.asList(Arrays.copyOfRange(set, 1, set.length))); - out.add(seth.toArray(new Integer[0])); - } - - return out; - } - } - ProposalTallyFactory factory = new ProposalTallyFactory(5, 23); - DeliberatorInterface mj = new MajorityJudgmentDeliberator(); - TallyInterface tally = ( - new Tally( - factory.generateAll() - ) - ); + TallyInterface tally = new Tally(factory.generateAll()); + DeliberatorInterface mj = new MajorityJudgmentDeliberator(); ResultInterface result = mj.deliberate(tally); - for (ProposalResultInterface proposalResult: result.getProposalResultsRanked()) { - System.out.print(proposalResult.getMerit().toString() + "\n"); + System.out.print( + "profile" + + "," + + "rank" + + "," + + "median" + + "," + + "merit" + ); + + for (ProposalResultInterface proposalResult : result.getProposalResultsRanked()) { + System.out.print( + "\n" + + "\"" + + Arrays.toString(proposalResult.getAnalysis().tally.getTally()) + + "\"" + + ", " + + proposalResult.getRank() + + ", " + + proposalResult.getAnalysis().getMedianGrade() + + ", " + + proposalResult.getMerit().toString() + ); } + } @Test diff --git a/src/test/java/fr/mieuxvoter/mj/ProposalTallyFactory.java b/src/test/java/fr/mieuxvoter/mj/ProposalTallyFactory.java new file mode 100644 index 0000000..058e5f2 --- /dev/null +++ b/src/test/java/fr/mieuxvoter/mj/ProposalTallyFactory.java @@ -0,0 +1,87 @@ +package fr.mieuxvoter.mj; + +import java.util.ArrayList; +import java.util.Arrays; +import java.util.List; + + +public class ProposalTallyFactory { + + private final Integer amountOfGrades; + private final Integer amountOfJudges; + + public ProposalTallyFactory( + Integer amountOfGrades, + Integer amountOfJudges + ) { + this.amountOfGrades = amountOfGrades; + this.amountOfJudges = amountOfJudges; + } + + /** + * Be careful, this method explodes quite fast. + * + * @return all the possible proposal tallies for amountOfGrades and amountOfJudges. + */ + public ProposalTallyInterface[] generateAll() { + ArrayList all = new ArrayList<>(); + + List tallies = multichoose(amountOfGrades, amountOfJudges); + for (Integer[] t : tallies) { + all.add(new ProposalTally(t)); + } + + return all.toArray(new ProposalTally[0]); + } + + /** + * All the ways to distribute k balls into n boxes. + * See Multiset on Wikipedia. + * + * @param n amount of boxes + * @param k amount of balls + */ + private List multichoose(Integer n, Integer k) { + assert n >= 0; + assert k >= 0; + + ArrayList out = new ArrayList<>(); + + if (k == 0) { + ArrayList set = new ArrayList<>(); + for (int i = 0; i < n; i++) { + set.add(0); + } + out.add(set.toArray(new Integer[0])); + return out; + } + + if (n == 0) { + return out; + } + + if (n == 1) { + ArrayList set = new ArrayList<>(); + set.add(k); + out.add(set.toArray(new Integer[0])); + return out; + } + + for (Integer[] set: multichoose(n-1, k)) { + ArrayList seth = new ArrayList<>(); + seth.add(0); + seth.addAll(Arrays.asList(set)); + out.add(seth.toArray(new Integer[0])); + } + + for (Integer[] set: multichoose(n, k-1)) { + ArrayList seth = new ArrayList<>(); + + seth.add(set[0] + 1); + seth.addAll(Arrays.asList(Arrays.copyOfRange(set, 1, set.length))); + out.add(seth.toArray(new Integer[0])); + } + + return out; + } +} \ No newline at end of file From 6f377ab7331acf77ad0266d90414532e489c6712 Mon Sep 17 00:00:00 2001 From: domi41 Date: Thu, 27 Mar 2025 14:30:26 +0100 Subject: [PATCH 03/19] feat: generate the merit distribution as CSV for further analysis 'tis exciting ! --- .../mj/MajorityJudgmentDeliberatorTest.java | 86 ++++++++++++------- 1 file changed, 56 insertions(+), 30 deletions(-) diff --git a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java index 6ba4cb3..1348a47 100644 --- a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java +++ b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java @@ -1,22 +1,25 @@ package fr.mieuxvoter.mj; -import static org.junit.jupiter.api.Assertions.*; - import net.joshka.junit.json.params.JsonFileSource; - import org.junit.jupiter.api.DisplayName; import org.junit.jupiter.api.Test; import org.junit.jupiter.api.function.Executable; import org.junit.jupiter.params.ParameterizedTest; -import java.math.BigInteger; -import java.util.ArrayList; -import java.util.List; -import java.util.Arrays; - import javax.json.JsonArray; import javax.json.JsonObject; import javax.json.JsonValue; +import java.io.BufferedWriter; +import java.io.IOException; +import java.math.BigInteger; +import java.nio.charset.StandardCharsets; +import java.nio.file.Files; +import java.nio.file.Path; +import java.nio.file.Paths; +import java.nio.file.StandardOpenOption; +import java.util.Arrays; + +import static org.junit.jupiter.api.Assertions.*; class MajorityJudgmentDeliberatorTest { @@ -482,39 +485,62 @@ void testNumericMerit() throws Throwable { } @Test - @DisplayName("Generate merit distribution CSV") + @DisplayName("Generate merit distribution CSV for study") void testMeritDistribution() throws Throwable { - ProposalTallyFactory factory = new ProposalTallyFactory(5, 23); + + // This test has no assertions. + // It is not a test, but a handy entrypoint for data generation. + // This ought to be moved somewhere else, probably another repo. + + Integer amountOfGrades = 7; + Integer amountOfJudges = 17; + ProposalTallyFactory factory = new ProposalTallyFactory(amountOfGrades, amountOfJudges); TallyInterface tally = new Tally(factory.generateAll()); DeliberatorInterface mj = new MajorityJudgmentDeliberator(); ResultInterface result = mj.deliberate(tally); - System.out.print( - "profile" - + "," - + "rank" - + "," - + "median" - + "," - + "merit" + StringBuilder stringBuilder = new StringBuilder(); + stringBuilder.append( + "profile" + + "," + + "rank" + + "," + + "median" + + "," + + "merit" ); for (ProposalResultInterface proposalResult : result.getProposalResultsRanked()) { - System.out.print( - "\n" - + "\"" - + Arrays.toString(proposalResult.getAnalysis().tally.getTally()) - + "\"" - + ", " - + proposalResult.getRank() - + ", " - + proposalResult.getAnalysis().getMedianGrade() - + ", " - + proposalResult.getMerit().toString() - ); + stringBuilder + .append("\n") + .append("\"") + .append(Arrays.toString(proposalResult.getAnalysis().tally.getTally())) + .append("\"") + .append(", ") + .append(proposalResult.getRank()) + .append(", ") + .append(proposalResult.getAnalysis().getMedianGrade()) + .append(", ") + .append(proposalResult.getMerit().toString()) + ; } + Path FILE_PATH = Paths.get(".", "merit_distribution.csv"); + try ( + BufferedWriter writer = Files.newBufferedWriter + ( + FILE_PATH, + StandardCharsets.UTF_8, + StandardOpenOption.CREATE, + StandardOpenOption.TRUNCATE_EXISTING + ) + ) { + writer.write(stringBuilder.toString()); + } catch (IOException e) { + System.err.println("Cannot write merit distribution to CSV file"); + e.printStackTrace(); + } } @Test From 578472d533923208c785d0290720632ab280c163 Mon Sep 17 00:00:00 2001 From: domi41 Date: Thu, 27 Mar 2025 14:36:00 +0100 Subject: [PATCH 04/19] docs --- .../java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java index 81ecb35..0a78a51 100644 --- a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java +++ b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java @@ -46,7 +46,7 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep Result result = new Result(); ProposalResult[] proposalResults = new ProposalResult[amountOfProposals]; - // I. Compute the scores of each Proposal + // I. Compute the score and merit of each Proposal for (int proposalIndex = 0; proposalIndex < amountOfProposals; proposalIndex++) { ProposalTallyInterface proposalTally = tallies[proposalIndex]; String score = computeScore(proposalTally, amountOfJudges); @@ -70,7 +70,7 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep proposalResultsSorted, (Comparator) (p0, p1) -> p1.getScore().compareTo(p0.getScore())); - // III. Attribute a rank to each Proposal and compute their merit + // III. Attribute a rank to each Proposal and compute their relative merit int rank = 1; for (int proposalIndex = 0; proposalIndex < amountOfProposals; proposalIndex++) { ProposalResult proposalResult = proposalResultsSorted[proposalIndex]; @@ -141,6 +141,7 @@ private String computeScore(ProposalTallyInterface tally, BigInteger amountOfJud /** * A higher score means a better rank. Assumes that grades' tallies are provided from "worst" * grade to "best" grade. This score is fast to compute but is not meaningful. + * For a meaningful scalar value, see computeMerit. * * @param tally Holds the tallies of each Grade for a single Proposal * @param amountOfJudges Amount of judges participating From 75f10d3db3174308480e15514a7491e42ee3b23d Mon Sep 17 00:00:00 2001 From: domi41 Date: Sun, 30 Mar 2025 17:54:22 +0200 Subject: [PATCH 05/19] feat: implement initial merit adjustment to affine MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This is very experimental, very fluid. Adjustment is commented out because right now it breaks the isomorphism due to numerical instability. (José!!!) --- .../mj/MajorityJudgmentDeliberator.java | 62 +++++++++++++++++++ .../mj/MajorityJudgmentDeliberatorTest.java | 2 +- 2 files changed, 63 insertions(+), 1 deletion(-) diff --git a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java index 0a78a51..696f90d 100644 --- a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java +++ b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java @@ -4,6 +4,8 @@ import java.util.Arrays; import java.util.Comparator; +import static java.lang.Math.*; + /** * Deliberate (rank proposals) using Majority Judgment. * @@ -42,7 +44,18 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep BigInteger amountOfJudges = tally.getAmountOfJudges(); Integer amountOfProposals = tally.getAmountOfProposals(); + BigInteger maxMerit = BigInteger.ONE; BigInteger sumOfMerits = BigInteger.ZERO; + + // O. Compute the (maximum!) merit a 100% EXCELLENT proposal would get. + if (tallies.length > 0) { + int amountOfGrades = tallies[0].getTally().length; + Integer[] bestTally = new Integer[amountOfGrades]; + Arrays.fill(bestTally, 0); + bestTally[bestTally.length - 1] = amountOfJudges.intValue(); + maxMerit = computeMerit(new ProposalTally(bestTally), amountOfJudges, this.favorContestation); + } + Result result = new Result(); ProposalResult[] proposalResults = new ProposalResult[amountOfProposals]; @@ -74,6 +87,7 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep int rank = 1; for (int proposalIndex = 0; proposalIndex < amountOfProposals; proposalIndex++) { ProposalResult proposalResult = proposalResultsSorted[proposalIndex]; + // Attribute the rank Integer actualRank = rank; if (proposalIndex > 0) { ProposalResult proposalResultBefore = proposalResultsSorted[proposalIndex - 1]; @@ -84,6 +98,8 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep proposalResult.setRank(actualRank); rank += 1; + // Affine the merit and compute the relative merit + //proposalResult.setMerit(adjustMerit(proposalResult.getMerit(), maxMerit)); proposalResult.computeMeritAsPercentage(sumOfMerits); } @@ -246,6 +262,52 @@ private BigInteger computeMerit( return merit; } + private BigInteger adjustMerit(BigInteger merit, BigInteger maxMerit) { + BigInteger adjustedMerit = BigInteger.ZERO.add(merit); // copy + + // We're cheating here, at the expense of numerical stability + // We could use a recursive Euclidean div ? + long precision = 1_000_000_000; + double meritNormalized = round(merit.multiply( + BigInteger.valueOf(precision * 10) + ).divide(maxMerit).doubleValue() / 10.0) / (double) precision; + + double rankNormalized = meritToRankModel(meritNormalized); + + adjustedMerit = BigInteger.valueOf(round( + (1.0 - rankNormalized) * (double) precision + )).multiply(maxMerit).divide( + BigInteger.valueOf(precision) + ); + + return adjustedMerit; + } + + private double meritToRankModel(double merit) { + int amountOfGrades = 7; // FIXME + + // Values derived from rough model fitting by hand ; they can be improved. + double[] amplitudes = new double[]{ + 0.358682, 1.09248, 1.69632, 1.61568, 0.95616, 0.2808, + }; + double tightness = 96.0; + + double rank = 0.0; // from 0.0 (exclusive) to 1.0 (inclusive) ; is 'double' enough precision? + for (int i = 0; i < amountOfGrades - 1; i++) { + rank += amplitudes[i] * sigmoid( + merit, + tightness, + (2.0 * i + 1.0) / (2.0 * (amountOfGrades - 1)) + ); + } + + return rank * (1.0 / (amountOfGrades - 1)); + } + + private double sigmoid(double x, double tightness, double origin) { + return 1.0 / (1.0 + pow(E, tightness * (x - origin))); + } + private int countDigits(int number) { return ("" + number).length(); } diff --git a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java index 1348a47..b3d1a6b 100644 --- a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java +++ b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java @@ -493,7 +493,7 @@ void testMeritDistribution() throws Throwable { // This ought to be moved somewhere else, probably another repo. Integer amountOfGrades = 7; - Integer amountOfJudges = 17; + Integer amountOfJudges = 11; ProposalTallyFactory factory = new ProposalTallyFactory(amountOfGrades, amountOfJudges); TallyInterface tally = new Tally(factory.generateAll()); From c6e87b65150c15e0cc95d7345d77fdd55ba0a1bf Mon Sep 17 00:00:00 2001 From: domi41 Date: Sun, 30 Mar 2025 18:00:42 +0200 Subject: [PATCH 06/19] fix: ensure tests pass --- .../fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java index 696f90d..614b8cb 100644 --- a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java +++ b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java @@ -44,15 +44,15 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep BigInteger amountOfJudges = tally.getAmountOfJudges(); Integer amountOfProposals = tally.getAmountOfProposals(); - BigInteger maxMerit = BigInteger.ONE; BigInteger sumOfMerits = BigInteger.ZERO; // O. Compute the (maximum!) merit a 100% EXCELLENT proposal would get. + BigInteger maxMerit = BigInteger.ONE; if (tallies.length > 0) { int amountOfGrades = tallies[0].getTally().length; - Integer[] bestTally = new Integer[amountOfGrades]; - Arrays.fill(bestTally, 0); - bestTally[bestTally.length - 1] = amountOfJudges.intValue(); + BigInteger[] bestTally = new BigInteger[amountOfGrades]; + Arrays.fill(bestTally, BigInteger.ZERO); + bestTally[bestTally.length - 1] = amountOfJudges; maxMerit = computeMerit(new ProposalTally(bestTally), amountOfJudges, this.favorContestation); } From b4eb40bd912574aeb29df1bc0e301a65c807c28c Mon Sep 17 00:00:00 2001 From: domi41 Date: Sun, 6 Apr 2025 01:12:19 +0200 Subject: [PATCH 07/19] feat: return both raw and affined merits --- .../mj/MajorityJudgmentDeliberator.java | 85 ++++++++++++++----- .../java/fr/mieuxvoter/mj/ProposalResult.java | 36 +++++++- .../mj/ProposalResultInterface.java | 4 + .../mj/MajorityJudgmentDeliberatorTest.java | 18 +++- 4 files changed, 118 insertions(+), 25 deletions(-) diff --git a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java index 614b8cb..b237e2a 100644 --- a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java +++ b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java @@ -45,6 +45,7 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep Integer amountOfProposals = tally.getAmountOfProposals(); BigInteger sumOfMerits = BigInteger.ZERO; + Double sumOfAdjustedMerits = 0.0; // O. Compute the (maximum!) merit a 100% EXCELLENT proposal would get. BigInteger maxMerit = BigInteger.ONE; @@ -98,9 +99,18 @@ public ResultInterface deliberate(TallyInterface tally) throws InvalidTallyExcep proposalResult.setRank(actualRank); rank += 1; - // Affine the merit and compute the relative merit - //proposalResult.setMerit(adjustMerit(proposalResult.getMerit(), maxMerit)); + // Adjust (make affine) the merit + proposalResult.setMeritAdjusted(adjustMerit( + proposalResult.getMerit(), maxMerit, amountOfJudges + )); + sumOfAdjustedMerits += proposalResult.getMeritAdjusted(); + } + + // Compute the relative merits + for (int proposalIndex = 0; proposalIndex < amountOfProposals; proposalIndex++) { + ProposalResult proposalResult = proposalResultsSorted[proposalIndex]; proposalResult.computeMeritAsPercentage(sumOfMerits); + proposalResult.computeMeritAdjustedAsPercentage(sumOfAdjustedMerits); } result.setProposalResults(proposalResults); @@ -262,36 +272,72 @@ private BigInteger computeMerit( return merit; } - private BigInteger adjustMerit(BigInteger merit, BigInteger maxMerit) { - BigInteger adjustedMerit = BigInteger.ZERO.add(merit); // copy - - // We're cheating here, at the expense of numerical stability + private Double adjustMerit(BigInteger merit, BigInteger maxMerit, BigInteger amountOfJudges) { + // We're "cheating" here, at the expense of numerical stability // We could use a recursive Euclidean div ? long precision = 1_000_000_000; double meritNormalized = round(merit.multiply( BigInteger.valueOf(precision * 10) ).divide(maxMerit).doubleValue() / 10.0) / (double) precision; - double rankNormalized = meritToRankModel(meritNormalized); + double rankNormalized = meritToRankModel(meritNormalized, amountOfJudges.intValue()); - adjustedMerit = BigInteger.valueOf(round( - (1.0 - rankNormalized) * (double) precision - )).multiply(maxMerit).divide( - BigInteger.valueOf(precision) - ); +// BigInteger adjustedMerit = BigInteger.ZERO.add(merit); // copy +// adjustedMerit = BigInteger.valueOf(round( +// (1.0 - rankNormalized) * (double) precision +// )).multiply(maxMerit).divide( +// BigInteger.valueOf(precision) +// ); +// return adjustedMerit; - return adjustedMerit; + return (1.0 - rankNormalized); } - private double meritToRankModel(double merit) { + private double meritToRankModel(double merit, Integer amountOfJudges) { int amountOfGrades = 7; // FIXME - // Values derived from rough model fitting by hand ; they can be improved. - double[] amplitudes = new double[]{ - 0.358682, 1.09248, 1.69632, 1.61568, 0.95616, 0.2808, + class SigmoidAmplitudeModel { + Double coeff; + Double offset; + Double origin; + + public SigmoidAmplitudeModel(Double coeff, Double offset, Double origin) { + this.coeff = coeff; + this.offset = offset; + this.origin = origin; + } + + public Double computeAmplitude(Integer amountOfJudges) { + return this.offset + (this.coeff / (amountOfJudges - this.origin)); + } + } + + // Values derived from rough model fitting ; they can be improved + SigmoidAmplitudeModel[] sam = new SigmoidAmplitudeModel[]{ + new SigmoidAmplitudeModel(0.5918756749697929, 0.0283650284831609, -1.1514768060735074), + new SigmoidAmplitudeModel(1.2239424469290872, 0.1482010931224683, -16.3552159899377614), + new SigmoidAmplitudeModel(-0.5592816818757540, 0.3123093902719977, -2.0931675704689443), + new SigmoidAmplitudeModel(-0.9888738957553507, 0.3136696647459276, -4.8529251973066447), + new SigmoidAmplitudeModel(-0.0370903838252796, 0.1591017470094314, -0.9399076517275036), + new SigmoidAmplitudeModel(0.2367789010429392, 0.0324575577968845, -0.8907160168896431), }; - double tightness = 96.0; + // Values derived from rough model fitting by hand ; they can be improved. +// double[] amplitudes = new double[]{ +// 0.358682, 1.09248, 1.69632, 1.61568, 0.95616, 0.2808, +// }; + + Double sumOfAmplitudes = 0.0; + Double[] amplitudes = new Double[amountOfGrades]; + for (int i = 0; i < amountOfGrades - 1; i++) { + amplitudes[i] = sam[i].computeAmplitude(amountOfJudges); + sumOfAmplitudes += amplitudes[i]; + } + for (int i = 0; i < amountOfGrades - 1; i++) { + amplitudes[i] = amplitudes[i] / sumOfAmplitudes; + } + + double tightness = 96.0; double rank = 0.0; // from 0.0 (exclusive) to 1.0 (inclusive) ; is 'double' enough precision? for (int i = 0; i < amountOfGrades - 1; i++) { rank += amplitudes[i] * sigmoid( @@ -301,7 +347,8 @@ private double meritToRankModel(double merit) { ); } - return rank * (1.0 / (amountOfGrades - 1)); + return rank; +// return rank * (1.0 / (amountOfGrades - 1)); } private double sigmoid(double x, double tightness, double origin) { diff --git a/src/main/java/fr/mieuxvoter/mj/ProposalResult.java b/src/main/java/fr/mieuxvoter/mj/ProposalResult.java index e1eade7..085472d 100644 --- a/src/main/java/fr/mieuxvoter/mj/ProposalResult.java +++ b/src/main/java/fr/mieuxvoter/mj/ProposalResult.java @@ -16,6 +16,10 @@ public class ProposalResult implements ProposalResultInterface { protected Double meritAsPercentage = 0.0; + protected Double meritAdjusted = 0.0; + + protected Double meritAdjustedAsPercentage = 0.0; + protected ProposalTallyAnalysis analysis; public Integer getIndex() { @@ -54,16 +58,44 @@ public Double getMeritAsPercentage() { return meritAsPercentage; } + public Double getMeritAdjusted() { + return meritAdjusted; + } + + public ProposalResult setMeritAdjusted(Double meritAdjusted) { + this.meritAdjusted = meritAdjusted; + return this; + } + + public Double getMeritAdjustedAsPercentage() { + return meritAdjustedAsPercentage; + } + public void computeMeritAsPercentage(BigInteger sumOfMerits) { if (sumOfMerits.compareTo(BigInteger.ZERO) == 0) { this.meritAsPercentage = 0.0; + this.meritAdjustedAsPercentage = 0.0; return; } + this.meritAsPercentage = divideAsPercentage(getMerit(), sumOfMerits); + } + + public void computeMeritAdjustedAsPercentage(Double sumOfAdjustedMerits) { + if (sumOfAdjustedMerits == 0) { + this.meritAdjustedAsPercentage = 0.0; + return; + } + + this.meritAdjustedAsPercentage = 100.0 * getMeritAdjusted() / sumOfAdjustedMerits; + } + + // This is a HACK ; improve it ! + private Double divideAsPercentage(BigInteger numerator, BigInteger denominator) { long precision = 1_000_000_000; // big enough for 7 billion humans - this.meritAsPercentage = round(this.getMerit().multiply( + return round(numerator.multiply( BigInteger.valueOf(100 * precision * 10) - ).divide(sumOfMerits).doubleValue() / 10.0) / (double) precision; + ).divide(denominator).doubleValue() / 10.0) / (double) precision; } public ProposalTallyAnalysis getAnalysis() { diff --git a/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java b/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java index b821b4e..2bbbf19 100644 --- a/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java +++ b/src/main/java/fr/mieuxvoter/mj/ProposalResultInterface.java @@ -29,6 +29,10 @@ public interface ProposalResultInterface { Double getMeritAsPercentage(); + Double getMeritAdjusted(); + + Double getMeritAdjustedAsPercentage(); + /** Get more data about the proposal tally, such as the median grade. */ ProposalTallyAnalysis getAnalysis(); } diff --git a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java index b3d1a6b..7cb6947 100644 --- a/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java +++ b/src/test/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberatorTest.java @@ -487,13 +487,16 @@ void testNumericMerit() throws Throwable { @Test @DisplayName("Generate merit distribution CSV for study") void testMeritDistribution() throws Throwable { + for (int i = 1; i < 41; i++) { + generateMeritDistribution(7, i); + } + } + void generateMeritDistribution(Integer amountOfGrades, Integer amountOfJudges) throws Throwable { // This test has no assertions. // It is not a test, but a handy entrypoint for data generation. - // This ought to be moved somewhere else, probably another repo. + // This ought to be moved somewhere else. - Integer amountOfGrades = 7; - Integer amountOfJudges = 11; ProposalTallyFactory factory = new ProposalTallyFactory(amountOfGrades, amountOfJudges); TallyInterface tally = new Tally(factory.generateAll()); @@ -509,6 +512,8 @@ void testMeritDistribution() throws Throwable { + "median" + "," + "merit" + + "," + + "merit_adjusted" ); for (ProposalResultInterface proposalResult : result.getProposalResultsRanked()) { @@ -523,10 +528,15 @@ void testMeritDistribution() throws Throwable { .append(proposalResult.getAnalysis().getMedianGrade()) .append(", ") .append(proposalResult.getMerit().toString()) + .append(", ") + .append(String.format("%.16f", proposalResult.getMeritAdjusted())) ; } - Path FILE_PATH = Paths.get(".", "merit_distribution.csv"); + Path FILE_PATH = Paths.get( + ".", + String.format("merit_distribution_%d_grades_%d_judges.csv", amountOfGrades, amountOfJudges) + ); try ( BufferedWriter writer = Files.newBufferedWriter ( From 1e1d2be593c83dd93a0a11df978a20c5dfd7acc5 Mon Sep 17 00:00:00 2001 From: domi41 Date: Tue, 8 Apr 2025 09:51:35 +0200 Subject: [PATCH 08/19] =?UTF-8?q?feat:=20improve=20the=20sigmo=C3=AFds=20a?= =?UTF-8?q?mplitude=20model=20with=20a=20sinuso=C3=AFd?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../mj/MajorityJudgmentDeliberator.java | 48 +++++++++++-------- 1 file changed, 29 insertions(+), 19 deletions(-) diff --git a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java index b237e2a..f20534e 100644 --- a/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java +++ b/src/main/java/fr/mieuxvoter/mj/MajorityJudgmentDeliberator.java @@ -297,36 +297,47 @@ private double meritToRankModel(double merit, Integer amountOfJudges) { int amountOfGrades = 7; // FIXME class SigmoidAmplitudeModel { - Double coeff; - Double offset; - Double origin; - - public SigmoidAmplitudeModel(Double coeff, Double offset, Double origin) { + final Double coeff; + final Double offset; + final Double origin; + final Double sin_ampli; + final Double sin_origin; + final Double sin_phase; + + public SigmoidAmplitudeModel( + Double coeff, + Double offset, + Double origin, + Double sin_ampli, + Double sin_origin, + Double sin_phase + ) { this.coeff = coeff; this.offset = offset; this.origin = origin; + this.sin_ampli = sin_ampli; + this.sin_origin = sin_origin; + this.sin_phase = sin_phase; } public Double computeAmplitude(Integer amountOfJudges) { - return this.offset + (this.coeff / (amountOfJudges - this.origin)); + return + this.offset + (this.coeff / (amountOfJudges - this.origin)) + + + this.sin_ampli * sin(amountOfJudges * PI + this.sin_phase) / (amountOfJudges - this.sin_origin); } } // Values derived from rough model fitting ; they can be improved SigmoidAmplitudeModel[] sam = new SigmoidAmplitudeModel[]{ - new SigmoidAmplitudeModel(0.5918756749697929, 0.0283650284831609, -1.1514768060735074), - new SigmoidAmplitudeModel(1.2239424469290872, 0.1482010931224683, -16.3552159899377614), - new SigmoidAmplitudeModel(-0.5592816818757540, 0.3123093902719977, -2.0931675704689443), - new SigmoidAmplitudeModel(-0.9888738957553507, 0.3136696647459276, -4.8529251973066447), - new SigmoidAmplitudeModel(-0.0370903838252796, 0.1591017470094314, -0.9399076517275036), - new SigmoidAmplitudeModel(0.2367789010429392, 0.0324575577968845, -0.8907160168896431), + new SigmoidAmplitudeModel(0.5151336373041772, 0.0304017096437998, -0.1560819745436698, -0.0642768687910415, 3.7019618565115722, -0.2267673450950530), + new SigmoidAmplitudeModel(0.8321495032592745, 0.1538010001096599, -10.1403742732170450, 0.1452337649130754, 2.9093303593527824, 0.1670760936959231), + new SigmoidAmplitudeModel(-0.5832534017217945, 0.3128738036537556, -2.4481699553712186, 1.7698591489043021, 0.0064898411429031, -3.1491904326892173), + new SigmoidAmplitudeModel(-0.9135479603269890, 0.3121169039235479, -4.0419384013683608, -0.0398619334678863, 2.2608983418537969, -3.5661704309341040), + new SigmoidAmplitudeModel(-0.0358891062680384, 0.1592742142625385, 0.8473094470570051, -0.1720450496934443, 0.8776512589952787, 0.1900715592340584), + new SigmoidAmplitudeModel(0.2965479931458628, 0.0309932939590777, -2.7064785369970221, -0.0616634512919992, 3.3069369590264279, -3.3295936102008192), }; - // Values derived from rough model fitting by hand ; they can be improved. -// double[] amplitudes = new double[]{ -// 0.358682, 1.09248, 1.69632, 1.61568, 0.95616, 0.2808, -// }; - Double sumOfAmplitudes = 0.0; Double[] amplitudes = new Double[amountOfGrades]; for (int i = 0; i < amountOfGrades - 1; i++) { @@ -337,7 +348,7 @@ public Double computeAmplitude(Integer amountOfJudges) { amplitudes[i] = amplitudes[i] / sumOfAmplitudes; } - double tightness = 96.0; + double tightness = 96.0; // derived from fitting double rank = 0.0; // from 0.0 (exclusive) to 1.0 (inclusive) ; is 'double' enough precision? for (int i = 0; i < amountOfGrades - 1; i++) { rank += amplitudes[i] * sigmoid( @@ -348,7 +359,6 @@ public Double computeAmplitude(Integer amountOfJudges) { } return rank; -// return rank * (1.0 / (amountOfGrades - 1)); } private double sigmoid(double x, double tightness, double origin) { From 8fc0ac9621bbe5424a9c85ec02dc8a276775b54b Mon Sep 17 00:00:00 2001 From: domi41 Date: Tue, 15 Apr 2025 13:31:15 +0200 Subject: [PATCH 09/19] docs: dump a markdown of the study of the scalar merit --- study/README.md | 890 ++++++++++++++++++++++++++++++++++++++++++ study/output_14_0.png | Bin 0 -> 334919 bytes study/output_18_0.png | Bin 0 -> 191812 bytes study/output_20_0.png | Bin 0 -> 94187 bytes study/output_22_0.png | Bin 0 -> 157164 bytes study/output_25_1.png | Bin 0 -> 192123 bytes study/output_30_0.png | Bin 0 -> 148225 bytes study/output_33_1.png | Bin 0 -> 178607 bytes study/output_7_0.png | Bin 0 -> 65390 bytes 9 files changed, 890 insertions(+) create mode 100644 study/README.md create mode 100644 study/output_14_0.png create mode 100644 study/output_18_0.png create mode 100644 study/output_20_0.png create mode 100644 study/output_22_0.png create mode 100644 study/output_25_1.png create mode 100644 study/output_30_0.png create mode 100644 study/output_33_1.png create mode 100644 study/output_7_0.png diff --git a/study/README.md b/study/README.md new file mode 100644 index 0000000..f268e41 --- /dev/null +++ b/study/README.md @@ -0,0 +1,890 @@ +# Scalar Merit Study + +## Goal + +The goal is to compute a meaningful _scalar merit_ value for each _merit profile_, so that [Majority Judgment](https://en.wikipedia.org/wiki/Majority_judgment) (MJ) may be used in [proportional representation](https://en.wikipedia.org/wiki/Proportional_representation). + +## Merit from Absolute Rank + +Every merit profile has an _absolute rank_, which is its rank in the MJ poll where all possible merit profiles (with the same amount of grades and judges) compete. + +A simple formula for a _scalar merit_ can therefore be: + +$ +Scalar\ Merit = Amount\ of\ Possible\ Merit\ Profiles - Absolute\ Rank +$ + +Sadly, the amount of possible merit profiles for a given amount of judges and grades grows big quite fast. Too fast. + +> 💡 Mathematically, a Merit Profile is a [Multiset](https://en.wikipedia.org/wiki/Multiset), so some work has been laid out already. + +$Amount\ of\ Possible\ Merit\ Profiles = \left(\!\!{n \choose k}\!\!\right) = {n+k-1 \choose k} = \frac{(n+k-1)!}{k!\,(n-1)!} = {n(n+1)(n+2)\cdots(n+k-1)\over k!}$ + +Where: +$ +\left\{ + \begin{array}{ll} + n = Amount\ of\ Grades = 7\ for\ example\\ + k = Amount\ of\ Judges = 40\ for\ example + \end{array} +\right. +$ + +Let's hack some Python to see how the amount of possible merit profiles behave: + + +```python +# Partial factorial ; set begin=1 for the regular factorial. +def factorial(begin: int, end: int) -> int: + assert(0 < begin <= end) + product: int = end + for coeff in range(begin, end): + product *= coeff + return product + + +# https://en.wikipedia.org/wiki/Multiset +# Returns the number of multisets of cardinality k, with elements taken from a finite set of cardinality n. +def multiset_coefficient(n: int, k: int) -> int: + assert(n > 0 and k > 0) + return factorial(n, n + k - 1) // factorial(1, k) +``` + + +```python +multiset_coefficient(7, 40) # Amount of possible merit profiles for 7 grades and 40 judges +``` + + + + + 9366819 + + + +Ranking 10 million merit profiles is still manageable, but what happens when you have $160\ 000$ judges ? + + +```python +lots = multiset_coefficient(7, 160_000) +print(len(str(lots)), "digits is too many fingers") +lots +``` + + 29 digits is too many fingers + + + + + + 23304747394848625835520392001 + + + +> 🔔 Now, **that's too many** merit profiles to rank them all in a single MJ poll in order to compute their absolute rank. + +Just for completion's sake, let's see how the amount of possible merit profiles grows with the amount of judges: + + +```python +import matplotlib.pyplot as plt +import numpy as np + +# Configure the plots +plt.style.use('dark_background') +plt.rcParams['figure.figsize'] = [20, 10] +``` + + +```python +sampling_size = 1000 +sampling = np.arange(1, sampling_size) + +# Oddity: this throws "RuntimeWarning: overflow encountered in scalar multiply" +#print([multiset_coefficient(7, i) for i in sampling]) + +# List of the amount of possible merit profiles, indexed by judges' amount, starting at 1. +# Not using the comprehension syntax because it overflows, somehow. +multiset_coefficients = [] +for i in range(1, sampling_size): + multiset_coefficients.append(multiset_coefficient(7, i)) + +from matplotlib.ticker import StrMethodFormatter + +plt.title("Evolution of the Amount of Possible Merit Profiles\nas the Amount of Judges increase, for 7 Grades") +plt.gca().yaxis.set_major_formatter(StrMethodFormatter('{x:,.0f}')) +plt.xlabel("Amount of Judges") +plt.ylabel("Amount of Possible Merit Profiles") +plt.plot( + sampling, + multiset_coefficients, +) +plt.show() +``` + + + +![png](output_7_0.png) + + + +As you can see, the numbers quickly grow to cosmic scales, and therefore this trivial technique for computing the _merit scalar_ of a merit profile won't "work" in practice, as sorting $10\ 000\ 000$ merit profiles using MJ already takes about a minute. + +Despair not, because if we can find an isomorphism of this technique that we _can_ compute, we'll manage. + +> Enters _Marc Paraire_. + +## Merit from Signed Base + +_Marc Paraire_ found a way to compute a meaningful, isomorphic merit scalar for a given merit profile. + +> 🎉 This is amazing, as it unlocks proportional representation using Majority Judgment. + +> _Signed Base_ is not a great name, but I do need one ; please share your ideas. + +We will study how that scalar merit is distributed over all possible merit profiles, and how the amount of grades and participants affect it. + +> We will focus on 7 grades for now, for simplicity's sake. + +Let's start by checking out the algorithm for computing that merit scalar : + + +### Overview of the Algorithm + +```mermaid +flowchart TD + +Score>Scalar Merit] +Start((Start)) +ForLoop{loop once
per grade left
in the set
eg. 6 times } +End((End)) + +BaseShift[Count Amount of Judges] +ComputeMedian[Compute Median Grade] +ComputeDecisionScore[Compute Decision Score] +Regrade[Regrade median
into current grade] + +Start --> ComputeMedian +ForLoop --> |end| End +ForLoop --> |loop| BaseShift +End -.- |read| Score +ComputeMedian -.- | add | Score +ComputeMedian --> ForLoop +ComputeDecisionScore -.- | add | Score +ComputeDecisionScore --> Regrade +BaseShift -.- | multiply | Score +BaseShift --> ComputeDecisionScore +Regrade --> ForLoop +``` + +#### Decision Score + +> Not fond of the name, feel free to suggest another. _Decision Strength_ ? … Meh. + +It's the **size of the biggest group** outside of the median grade, signed. +It's positive if it is an _adhesion group_ (higher than the median), and negative if it's a _contestation group_. + +This value will always be in the range $]-\frac{Amount\ of\ Judges} 2, \frac{Amount\ of\ Judges} 2]$, which is why using a base $Amount\ of\ Judges$ works so well. + + + +### Collect the Data + +The `CSV` files were generated using _Java_, following these steps: + +1. Generate all possible merit profiles for $7$ grades and $k$ judges. +2. Rank them using _Majority Judgment_. +3. Compute their individual _Scalar Merit_ using the _Signed Base_ technique. +4. Generate a `CSV` file. + +> Generating this data using Python would be better, but we need to improve the Python MJ library first. + + + +```python +from tools import read_data, deviation_between, affine_data, np_sigmoid + +# Datasets we want to use +grades_amount = 7 # I've only generated the datasets for 7 grades +distributions_to_plot = [ + { 'grades': grades_amount, 'judges': i } for i in range(1, 41) +] + +# Read data from CSV(s) +rank_datas = [] +merit_datas = [] +for i, config in enumerate(distributions_to_plot): + merit_data, rank_data = read_data( + "./merit_distribution_%d_grades_%d_judges.csv"%(config['grades'], config['judges']), + limit = 0, + ) + rank_datas.append(rank_data) + merit_datas.append(merit_data) +``` + +### Plot the Merit + +Here, we're going to plot the merits for various $K$ judges. + + + +```python +plt.title("Merit Distribution (%d grades)" % (grades_amount,)) + +# Axes Configuration +plt.xlabel('rank') +plt.xticks([0.0, 0.5, 1.0], ["Best", "Middle", "Worst"]) +plt.ylabel('merit (normalized)') +plt.yticks( + np.linspace(0.0, 1.0, grades_amount), + ["0"] + ["%d/%d" % (i, grades_amount - 1) for i in range(1, grades_amount - 1)] + ["1"], +) + +for i, config in enumerate(distributions_to_plot): + plt.plot( + rank_datas[i], merit_datas[i], + marker='.', + ls='None', + label="Raw Merit %d judges (σ=%.2f%%)" % ( + config['judges'], + deviation_between(merit_datas[i], affine_data(rank_datas[i])) * 100.0, + ), + ) + +# Ideal Affine Data +plt.plot( + rank_datas[0], affine_data(rank_datas[0]), + label="Ideal Affine Merit (σ=0%)", +) + +plt.grid() +plt.legend(loc='center left', bbox_to_anchor=(1, 0.5)) +plt.show() +``` + + + +![png](output_14_0.png) + + + +Observations: + +- the amount of judges changes the shape of the curve +- the shape seems to converge as we add more and more judges +- the multiples of $\frac 1 6$ are the merit profiles with 100% of the judges casting the same grade + +We can also observe that the distribution is not affine (linear), as it would be with _Merit from Absolute Rank_, except in the trivial case with only $1$ judge. + + +### Adjusting the Merit Curve to make it Affine + +If we can approximate well enough the inverse with an analytical function, we can adjust the merit curve to make it affine. + +The first step is to fit the inverse, then. + +### Fitting the Inverse + +Let's start by plotting the inverses : + + +```python +plt.title("Merit Inverses (%d grades)" % (grades_amount,)) + +# Axes Configuration +plt.xlabel('merit (normalized)') +plt.xticks( + np.linspace(0.0, 1.0, grades_amount), + ["0"] + ["%d/%d" % (i, grades_amount - 1) for i in range(1, grades_amount - 1)] + ["1"], +) +plt.ylabel('rank') +plt.yticks([0.0, 0.5, 1.0], ["Best", "Middle", "Worst"]) + + +for i, config in enumerate(distributions_to_plot): + if i > 10 and i < 39 : continue + plt.plot( + merit_datas[i], rank_datas[i], + marker='.', + ls='None', + label="Raw Merit %d judges (σ=%.2f%%)" % ( + config['judges'], + deviation_between(merit_datas[i], affine_data(rank_datas[i])) * 100.0, + ), + ) + +# Ideal Affine Data +plt.plot( + rank_datas[0], affine_data(rank_datas[0]), + label="Ideal Affine Merit (σ=0%)", +) + +plt.grid() +plt.legend(loc="upper right") +plt.show() +``` + + + +![png](output_18_0.png) + + + +We can fit the curve for a given amount of judges using a sigmoïd series. + +For example, for $17$ judges : + + +```python +plt.title("Hand-Fitting a Sigmoid Series\non the Merit Inverse") + +# Hand fitted for 17 judges +def sigmoid_hand_model(amount_of_judges): + tightness = 96 + amplis = [0.358682, 1.09248, 1.69632, 1.61568, 0.95616, 0.2808] + return (1.0/6.0) * sum( + amplis[i] * np_sigmoid(merit_datas[amount_of_judges-1], tightness=tightness, origin=(2.0*i+1.0)/12.0) + for i in range(6) + ) + +model_17 = sigmoid_hand_model(17) +model_11 = sigmoid_hand_model(11) +model_40 = sigmoid_hand_model(40) + +# Axes Configuration +plt.xlabel('merit (normalized)') +plt.xticks( + np.linspace(0.0, 1.0, grades_amount), + ["0"] + ["%d/%d" % (i, grades_amount - 1) for i in range(1, grades_amount - 1)] + ["1"], +) +plt.ylabel('rank') +plt.yticks([0.0, 0.5, 1.0], ["Best", "Middle", "Worst"]) + +# Data 17 judges +plt.plot( + merit_datas[16], rank_datas[16], + marker='.', + ls='None', + label="Raw Merit %d judges (σ=%.2f%%)" % ( + 17, + deviation_between(rank_datas[16], model_17) * 100.0, + ), +) + +# Data 11 judges +plt.plot( + merit_datas[10], rank_datas[10], + marker='.', + ls='None', + label="Raw Merit %d judges (σ=%.2f%%)" % ( + 10, + deviation_between(rank_datas[10], model_11) * 100.0, + ), +) + +# Data 40 judges +plt.plot( + merit_datas[39], rank_datas[39], + marker='.', + ls='None', + label="Raw Merit %d judges (σ=%.2f%%)" % ( + 39, + deviation_between(rank_datas[39], model_40) * 100.0, + ), +) + +# Hand fitted model (for 17 judges) +plt.plot(merit_datas[16], + model_17, + 'r-', + label="Hand-Fitted Model for 17 judges", +) + +plt.grid() +plt.legend(loc="upper right") +plt.show() +``` + + + +![png](output_20_0.png) + + + +Since the amount of judges changes the "amplitude" of the sigmoids, let's study how the amplitude of the sigmoids behave when the amount of judges change : + + +```python +plt.title("Evolution of the amplitude of the sigmoïds as we add more judges") +plt.xlabel("Amount of Judges") +plt.ylabel("Sigmoid Amplitude\nin Normalized Rank") + +whole_merits = np.linspace(0.0, 1.0, grades_amount) +for whole_merit_index, section in enumerate(whole_merits[:-1]): + next_section = whole_merits[whole_merit_index+1] + sigmoid_amplitudes = [ + np.interp(section, merit_datas[i][::-1], rank_datas[i][::-1]) - np.interp(next_section, merit_datas[i][::-1], rank_datas[i][::-1]) + for i in range(len(merit_datas)) + ] + + plt.plot( + [d['judges'] for d in distributions_to_plot], + sigmoid_amplitudes, + label="Sigmoid Amplitude (section %.2f to %.2f)" % (section,next_section), + ) + +plt.grid() +plt.legend() +plt.show() +``` + + + +![png](output_22_0.png) + + + +Wow. If we want to model these curves, we should ignore all the cases below, let's say, $10$ judges, because of the chaotic behavior of the curves and the fact that $10$ judges yield $8008$ possible merit profiles, and so we can embed the data in the algorithm and compute directly the _absolute rank_ of each profile, which is already the best merit scalar we can compute. + +### Empirically Fitting the Sigmoids' Amplitudes + + +```python +import math +from symfit import parameters, variables, sin, cos, exp, Fit, Eq, Le +from symfit.core.minimizers import BasinHopping, BFGS, SLSQP + +plt.title("Fitting the sigmoïds' amplitudes") +plt.xlabel("Amount of Judges") +plt.ylabel("Sigmoid Amplitude\nin Normalized Rank") + +skip_first_n = 4 + +judges_data = np.array([d['judges'] for d in distributions_to_plot[skip_first_n:]]) +sigmoids_amplitudes = [] + +# Sigmoid Amplitude Model +x, y = variables('x, y') +coeff, offset, origin = parameters('coeff, offset, origin') +sin_phase, sin_ampli, sin_origin = parameters('sin_phase, sin_ampli, sin_origin') +sigmampli_model_dict = { + y: ( + coeff / (x - origin) + offset + sin_ampli * sin(x * math.pi + sin_phase) / (x - sin_origin) + ), +} +sigmampli_params = [] + +sections = np.linspace(0.0, 1.0, grades_amount) +for section_index, section in enumerate(sections[:-1]): + next_section = sections[section_index + 1] + sigmoid_amplitudes = np.array([ + np.interp(section, merit_datas[i][::-1], rank_datas[i][::-1]) - np.interp(next_section, merit_datas[i][::-1], rank_datas[i][::-1]) + for i in range(skip_first_n, len(merit_datas)) + ]) + sigmoids_amplitudes.append(sigmoid_amplitudes) + + # Plot the Data + plot_lines = plt.plot( + judges_data, + sigmoid_amplitudes, + marker='.', + ls='None', + label="Sigmoid Amplitude (section %.2f to %.2f)" % (section, next_section), + ) + section_color = plot_lines[0].get_color() + + # Fit our Model to the Data + fit = Fit( + sigmampli_model_dict, + x=judges_data, + y=sigmoid_amplitudes, + minimizer=[BasinHopping, SLSQP], + ) + fit_result = fit.execute(BasinHopping={'niter': 300}) + sigmampli_params.append(dict(fit_result.params)) + + # Plot the Model + plt.plot( + judges_data, + fit.model(x=judges_data, **fit_result.params).y, + ls='--', + color=section_color, + label="Model σ=%.2f%%" % ( + deviation_between(fit.model(x=judges_data, **fit_result.params).y, sigmoid_amplitudes)*100.0, + ), + ) + + # Plot the Model Asymptote + plt.plot( + judges_data, + np.full(judges_data.shape, fit_result.params['offset']), + color=section_color, + ls="-.", + label="Model Asymptote at %.4f" % ( + fit_result.params['offset'], + ), + ) + +print("Sigmoids Amplitude Model Params") +print("y =", sigmampli_model_dict[y]) +print(sigmampli_params) + +# Dump for Java +for p in sigmampli_params: + print("new SigmoidAmplitudeModel(%.16f, %.16f, %.16f, %.16f, %.16f, %.16f)," % ( + p['coeff'], + p['offset'], + p['origin'], + p['sin_ampli'], + p['sin_origin'], + p['sin_phase'], + )) + + +plt.grid() +plt.legend(loc='center left', bbox_to_anchor=(1, 0.5)) +plt.show() +``` + + Sigmoids Amplitude Model Params + y = coeff/(-origin + x) + offset + sin_ampli*sin(sin_phase + 3.14159265358979*x)/(-sin_origin + x) + [{'coeff': 0.5148301383493251, 'offset': 0.030410388230188688, 'origin': -0.1524186984917907, 'sin_ampli': 2.205940441126818, 'sin_origin': 3.7050024705904643, 'sin_phase': 0.006544665723088311}, {'coeff': 0.8551817626947592, 'offset': 0.15342174631491304, 'origin': -10.516959046473387, 'sin_ampli': 2.0963433628559636, 'sin_origin': 2.657351955747391, 'sin_phase': 0.012335385036750999}, {'coeff': -0.5834237850939339, 'offset': 0.3128774375272333, 'origin': -2.4509363288243864, 'sin_ampli': -7.8681093539820735, 'sin_origin': 0.0892054917789014, 'sin_phase': 3.143285142800352}, {'coeff': -0.9262282737155574, 'offset': 0.312388586697186, 'origin': -4.178188331401861, 'sin_ampli': -1.5881189399431324, 'sin_origin': 1.1027152246988985, 'sin_phase': 0.01260604488766604}, {'coeff': -0.03728692233363923, 'offset': 0.15932564255813447, 'origin': 0.7047012094837567, 'sin_ampli': 0.04735122531333241, 'sin_origin': 1.1959469017105955, 'sin_phase': -0.7135586753713631}, {'coeff': 0.2931662497402955, 'offset': 0.031042329824810214, 'origin': -2.5537377586722614, 'sin_ampli': -0.036832920968138956, 'sin_origin': 2.410742818542175, 'sin_phase': 0.41483793094208793}] + new SigmoidAmplitudeModel(0.5148301383493251, 0.0304103882301887, -0.1524186984917907, 2.2059404411268182, 3.7050024705904643, 0.0065446657230883), + new SigmoidAmplitudeModel(0.8551817626947592, 0.1534217463149130, -10.5169590464733869, 2.0963433628559636, 2.6573519557473908, 0.0123353850367510), + new SigmoidAmplitudeModel(-0.5834237850939339, 0.3128774375272333, -2.4509363288243864, -7.8681093539820735, 0.0892054917789014, 3.1432851428003521), + new SigmoidAmplitudeModel(-0.9262282737155574, 0.3123885866971860, -4.1781883314018611, -1.5881189399431324, 1.1027152246988985, 0.0126060448876660), + new SigmoidAmplitudeModel(-0.0372869223336392, 0.1593256425581345, 0.7047012094837567, 0.0473512253133324, 1.1959469017105955, -0.7135586753713631), + new SigmoidAmplitudeModel(0.2931662497402955, 0.0310423298248102, -2.5537377586722614, -0.0368329209681390, 2.4107428185421749, 0.4148379309420879), + + + + +![png](output_25_1.png) + + + +_Not too shabby_ ; yet the model may still be improved. +We especially need to figure out the _correct_ asymptotes, so that extrapolation is meaningful. + +### Dump the initial values for use in algorithms + + +```python +for i in range(1, 9): + print("// Sigmoids Amplitudes for %d judges" % (i+1,)) + print("new Double[]{%s}," % (", ".join(str(sigmoids_amplitudes[e][i]) for e in range(grades_amount-1)),)) +``` + + // Sigmoids Amplitudes for 2 judges + new Double[]{0.12026002166847238, 0.21235102925243765, 0.24593716143011923, 0.21668472372697722, 0.14409534127843987, 0.06067172264355364}, + // Sigmoids Amplitudes for 3 judges + new Double[]{0.09737609329446062, 0.1959183673469388, 0.24897959183673468, 0.23323615160349856, 0.15918367346938775, 0.0653061224489796}, + // Sigmoids Amplitudes for 4 judges + new Double[]{0.09760159893404396, 0.20519653564290474, 0.25882744836775484, 0.2331778814123917, 0.14923384410393073, 0.05596269153897402}, + // Sigmoids Amplitudes for 5 judges + new Double[]{0.08373301358912866, 0.1930455635491607, 0.26019184652278177, 0.2448041566746603, 0.15947242206235013, 0.05875299760191847}, + // Sigmoids Amplitudes for 6 judges + new Double[]{0.08380167353565626, 0.19932559010865492, 0.26751592356687903, 0.24478581241413763, 0.15211689771449982, 0.05245410266017235}, + // Sigmoids Amplitudes for 7 judges + new Double[]{0.07458585858585853, 0.19006060606060615, 0.2681212121212121, 0.2534141414141414, 0.15951515151515153, 0.054303030303030304}, + // Sigmoids Amplitudes for 8 judges + new Double[]{0.07461078489468298, 0.1945806173571082, 0.2737704034908151, 0.2534073156278619, 0.15385444163120185, 0.04977643699833001}, + // Sigmoids Amplitudes for 9 judges + new Double[]{0.06807710736795547, 0.18731340532969665, 0.27400390696988686, 0.2600715049205706, 0.15944860123106408, 0.05108547418082636}, + + +### Adjust the Merit Distribution to make it Quasi-Affine + +Let's implement the sigmoid series in Java and apply it as _affine adjustment_ to the merit. + +Here's what our inverse model looks like : + +$$ +n = Amount\ of\ Grades +$$ +$$ +k = Amount\ of\ Judges +$$ +$$ +t = 96\ \ \tiny(fitted) +$$ +$$ +\left\{ + \begin{array}{ll} + a_i = \frac{coeff_i}{k-origin_i} + offset_i + sin(\pi k+sin\_phase_i) \frac{sin\_ampli_i}{k-sin\_origin_i}\ \ \tiny(fitted),\ if\ k > 10\\ + a_i = from\ data\ \ \tiny(gathered),\ if\ k \le 10 + \end{array} +\right. +$$ +$$ +y = \sum_{i=1}^{n - 1} \frac{a_i}{1 + e^{t(x - \frac{2i+1}{2(n-1)})}} +$$ + +The new distribution of the adjusted merit is much more linear: + + + +```python +plt.title("Quasi-Affine Merit Distribution\nAdjusted via Inverse Fitting") + +plt.plot( + rank_data, affine_data(rank_data), + label="Ideal Affine Merit (σ=0%)", +) + +raw_merit_index = len(distributions_to_plot) - 1 +plt.plot( + rank_datas[raw_merit_index], merit_datas[raw_merit_index], + marker='.', + ls='None', + color='grey', + label="Raw Merit, for reference (σ=%.2f%%)" % ( + # distributions_to_plot[raw_merit_index]['judges'], + deviation_between(merit_datas[raw_merit_index], affine_data(rank_datas[raw_merit_index])) * 100.0, + ), +) + +for i in range(30, 40): + rank_data, merit_adjusted_data = read_data( + filepath="merit_distribution_7_grades_%d_judges.csv" % (i,), + x_column="rank", + y_column="merit_adjusted", + y_type='float', + ) + + plt.plot( + rank_data, merit_adjusted_data, + label="Affined Merit %d judges (σ=%.2f%%)" % ( + i, + deviation_between(merit_adjusted_data, affine_data(rank_data)) * 100.0, + ), + ) + +plt.xlabel('rank') +plt.xticks([0.0, 0.5, 1.0], ["Best", "Middle", "Worst"]) +plt.ylabel('merit (normalized)') +plt.yticks( + np.linspace(0.0, 1.0, grades_amount), + ["0"] + ["%d/%d" % (i, grades_amount - 1) for i in range(1, grades_amount - 1)] + ["1"], +) +plt.legend(loc="upper right") +plt.grid() +plt.show() +``` + + + +![png](output_30_0.png) + + + +This pretty _scoubidou_ can be flattened further by improving our model. + +> We will need to implement the algos in python to speed up the process though. + +## Fairness Constraints + +### Extreme Brigadism + +Rida Laraki reported a first, simple constraint about extreme brigadism cases. + +Let's see how these merit profiles are _(absolutely)_ ranked. + + + +```python +plt.rcParams['figure.figsize'] = [16.18, 10] + +plt.title("Various Merit Distributions") + +# Desired amount of judges for this plot +k = 20 + +# raw_merit_index = len(distributions_to_plot) - 1 +raw_merit_index = k-1 +plt.plot( + rank_datas[raw_merit_index], merit_datas[raw_merit_index], + marker='.', + ls='None', + color='grey', + label="Computable Merit, for reference", +) + +plt.plot( + rank_data, affine_data(rank_data), + label="Ideal Affine Merit",# (σ=0%)", +) + + +rank_data, merit_adjusted_data = read_data( + filepath="merit_distribution_7_grades_%d_judges.csv" % (k,), + x_column="rank", + y_column="merit_adjusted", + y_type='float', + limit=0, +) + +raw_rank_data, profiles_data = read_data( + filepath="merit_distribution_7_grades_%d_judges.csv" % (k,), + x_column="rank", + y_column="profile", + y_type='str', + normalized=False, + limit=0, +) + +print(f"{len(rank_data)} Merit Profiles") +assert(len(rank_data) == len(profiles_data)) + +# Like np.where(), but working ; this is NOT the JM sort, it's … numpy's API +profiles_sorter = np.argsort(profiles_data) +def where_profiles(profiles_to_match): + return profiles_sorter[np.searchsorted(profiles_data, profiles_to_match, sorter=profiles_sorter)] + +def plot_distribution_constraint( + label: str, + form: str, + profiles, + expected_merits, + color = "#ff3399", +): + ranks = rank_data[where_profiles(profiles)] + plt.vlines( + x=ranks, + ymin=np.zeros(ranks.shape), + ymax=expected_merits, + color=color, + linestyles='dotted', + label=f"{label} of the form {form}", + ) + plt.plot( + ranks, + expected_merits, + color=color, + label=f"Ideal Merit to Stay Fair with {label}", + ) + +extremely_brigaded_profiles_color = "#ff3399" +extremely_brigaded_profiles = np.asarray([str([j, 0, 0, 0, 0, 0, k-j]) for j in range(k+1)]) +print(len(extremely_brigaded_profiles),"Extremely Brigaded Merit Profiles",extremely_brigaded_profiles) + +plot_distribution_constraint( + label="Extremely Brigaded Merit Profiles", + # form="[i, 0, 0, 0, 0, 0, k-i] for i in [0,k]", + form=r"$(i, 0, 0, 0, 0, 0, k-i)\ \forall\ i \in [\![0,k]\!]$", + profiles=extremely_brigaded_profiles, + expected_merits=np.linspace(1.0, 0.0, len(extremely_brigaded_profiles)), # we want same as uninominal + color=extremely_brigaded_profiles_color, +) + +# WIP : meh, no expected merits +# half_brigaded_profiles = np.asarray([str([j, i//8, i//8, i//8, i//8, i//8, (i//2-j)]) for j in range(i//2+1)]) +# print(len(half_brigaded_profiles),"Half Brigaded Merit Profiles",half_brigaded_profiles) +# plot_distribution_constraint( +# label="Half Brigaded Merit Profiles", +# form="[i, 1, 1, 1, 1, 1, (k/2-i)] for i in [0,k/2[", +# profiles=half_brigaded_profiles, +# expected_merits=np.linspace(1.0, 0.0, len(half_brigaded_profiles)), +# color="#ff9933", +# ) + +if k > 5: + mostly_brigaded_profiles = np.asarray([str([j, 1, 1, 1, 1, 1, (k-5-j)]) for j in range(k-5+1)]) + print(len(mostly_brigaded_profiles), "Mostly Brigaded Merit Profiles", mostly_brigaded_profiles) + + plot_distribution_constraint( + label="Mostly Brigaded Merit Profiles", + # form="[i, 1, 1, 1, 1, 1, (k-5-i)] for i in [0,k-5]", + form=r"$(i, 1, 1, 1, 1, 1, k-5-i)\ \forall\ i \in [\![0,k-5]\!]$", + profiles=mostly_brigaded_profiles, + # expected_merits=np.linspace(1.0, 0.0, len(mostly_brigaded_profiles)), # incorrect + expected_merits=(np.linspace(1.0, 0.0, len(mostly_brigaded_profiles))-0.5)*0.82+0.5, # wip - magic number -_- + color="#ff9933", + ) + +wholly_graded_profiles_color = "#998877" +wholly_graded_profiles = np.asarray([str(np.roll([k, 0, 0, 0, 0, 0, 0], j).tolist()) for j in range(grades_amount)]) +print(len(wholly_graded_profiles), "Wholly Graded Merit Profiles", wholly_graded_profiles) + +plot_distribution_constraint( + label="Wholly Graded Merit Profiles", + form="roll([k, 0, 0, 0, 0, 0, 0], i) for i in [0,n[", + profiles=wholly_graded_profiles, + expected_merits=np.linspace(0, 1.0, len(wholly_graded_profiles)), + color=wholly_graded_profiles_color, +) + + +plt.xlabel(fr"All ${len(profiles_data)}$ possible Merit Profiles " + + fr"for $n={grades_amount}$ grades and $k={k}$ judges," + + f"\nranked from Best to Worst using Majority Judgment") +plt.xticks([0.0, 0.5, 1.0], ["Best", "Middle", "Worst"]) +plt.ylabel("Merit (normalized)") +plt.yticks( + np.linspace(0.0, 1.0, grades_amount), + ["0"] + ["%d/%d" % (i, grades_amount - 1) for i in range(1, grades_amount - 1)] + ["1"], +) +plt.legend(loc="upper center") +plt.grid() +plt.show() +``` + + 230230 Merit Profiles + 21 Extremely Brigaded Merit Profiles ['[0, 0, 0, 0, 0, 0, 20]' '[1, 0, 0, 0, 0, 0, 19]' + '[2, 0, 0, 0, 0, 0, 18]' '[3, 0, 0, 0, 0, 0, 17]' + '[4, 0, 0, 0, 0, 0, 16]' '[5, 0, 0, 0, 0, 0, 15]' + '[6, 0, 0, 0, 0, 0, 14]' '[7, 0, 0, 0, 0, 0, 13]' + '[8, 0, 0, 0, 0, 0, 12]' '[9, 0, 0, 0, 0, 0, 11]' + '[10, 0, 0, 0, 0, 0, 10]' '[11, 0, 0, 0, 0, 0, 9]' + '[12, 0, 0, 0, 0, 0, 8]' '[13, 0, 0, 0, 0, 0, 7]' + '[14, 0, 0, 0, 0, 0, 6]' '[15, 0, 0, 0, 0, 0, 5]' + '[16, 0, 0, 0, 0, 0, 4]' '[17, 0, 0, 0, 0, 0, 3]' + '[18, 0, 0, 0, 0, 0, 2]' '[19, 0, 0, 0, 0, 0, 1]' + '[20, 0, 0, 0, 0, 0, 0]'] + 16 Mostly Brigaded Merit Profiles ['[0, 1, 1, 1, 1, 1, 15]' '[1, 1, 1, 1, 1, 1, 14]' + '[2, 1, 1, 1, 1, 1, 13]' '[3, 1, 1, 1, 1, 1, 12]' + '[4, 1, 1, 1, 1, 1, 11]' '[5, 1, 1, 1, 1, 1, 10]' '[6, 1, 1, 1, 1, 1, 9]' + '[7, 1, 1, 1, 1, 1, 8]' '[8, 1, 1, 1, 1, 1, 7]' '[9, 1, 1, 1, 1, 1, 6]' + '[10, 1, 1, 1, 1, 1, 5]' '[11, 1, 1, 1, 1, 1, 4]' + '[12, 1, 1, 1, 1, 1, 3]' '[13, 1, 1, 1, 1, 1, 2]' + '[14, 1, 1, 1, 1, 1, 1]' '[15, 1, 1, 1, 1, 1, 0]'] + 7 Wholly Graded Merit Profiles ['[20, 0, 0, 0, 0, 0, 0]' '[0, 20, 0, 0, 0, 0, 0]' + '[0, 0, 20, 0, 0, 0, 0]' '[0, 0, 0, 20, 0, 0, 0]' + '[0, 0, 0, 0, 20, 0, 0]' '[0, 0, 0, 0, 0, 20, 0]' + '[0, 0, 0, 0, 0, 0, 20]'] + + + + +![png](output_33_1.png) + + + +In red, that's the distribution we need to validate the identity with uninominal, in extreme brigadism cases. + +Resilience to brigadism requires that my lower judgments don't affect the candidate with my highest judgment(s). +Computing the merit from the profiles will never be able to "validate" this rule. + +## Conclusion + +Perhaps show multiple proportions and let users choose ? + +### Absolute Rank (for Scouts) + +- All judgments cast have the (ideally exact) same impact. +- Approximation. +- Weak to brigadism. + +### 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