# Legislatures Elected by Evaluative Proportional Representation (EPR): An Algorithm

Journal of Political Risk, Vol. 8, No. 1, January 2020

Source: Pixabay

Stephen Bosworth, Anders Corr, Stevan Leonard1

Abstract

Unlike existing voting methods, this article describes a new method that gives all voters every appropriate reason to be pleased. Evaluative Proportional Representation (EPR) invites each citizen to grade the suitability for office of any number of candidates as either Excellent (ideal), Very Good, Good, Acceptable, Poor, or “Reject” (completely unsuitable).  EPR allows each citizen to guarantee that one of the elected members of the legislature has received either their highest grade, remaining highest grade, or proxy vote – no vote is needlessly wasted.

# Introduction

The rounds in Stage 1 of EPR’s count provisionally determine the number of highest grades (votes) each candidate has exclusively received from all the voters. Each round discovers how many votes a different candidate has received.  If a voter has given the same grade to more than one candidate, it is given exclusively to the candidate who would have the largest total as a result.  This is justified by the democratic assumption that, other things being equal, the candidate who has received the largest number of equal or higher evaluations at that point in the count is probably the most qualified for office.

However, no winner is allowed to retain enough votes to dictate to the legislature. Therefore, our simulated election limits the percent of votes any winner can retain to 20%. This ensures that at least three members of the legislature will have to agree for any majority decision to be made. We call a candidate who has received such a percentage super popular. In Stage 2 of the count, any non-super-popular candidate is eligible to receive at least one of the extra votes initially held by a super-popular candidate. The winning number of candidates are those who have received the largest numbers of these highest or remaining highest grades by the beginning of Stage 3.

Of course, voting using existing methods is still very important, at least as a performance of a civic duty. Additionally, it is praiseworthy when a citizen votes in an attempt to make a constructive contribution to the democratic life of one’s community. However, we also assume that each voter desires that their own concerns, values, and ideas be accurately represented in the legislative body. Unfortunately and needlessly, all of the existing voting methods do not fully guarantee this level of representation. Consequently, many citizens have very good reasons to be displeased because their votes have been needlessly wasted in one or both of the two senses defined next.

# Votes Wasted Quantitatively and Qualitatively

We see a citizen’s vote as entirely wasted quantitatively when it does not help elect any candidate they see as at least acceptable.  Also, when each representative has only one vote in the legislature, a citizen’s vote is partly wasted quantitatively when it is given but not needed to elect one’s favored representative.  If instead this representative had a weighted vote in the legislature equal to the total number of votes they received from citizens as provided by EPR, no quantitative waste would occur.  Each citizen’s vote would continue to count equally and proportionately.

A citizen’s vote is entirely wasted qualitatively when it helps to elect a candidate they view as unacceptable.  A vote is partially wasted qualitatively to the extent that it helps elect a candidate seen by a voter as less fit for office than the alternative they trust most to speak, work, and vote as they would themselves if they had the time, energy, skills and opportunity to do so. EPR provides all voters with a meaningful qualitative and comfortable common language using the above six different grades to express their judgments of any number of the candidates.  EPR minimizes qualitative waste, which might unavoidably result from vote transfers or proxy votes.  Only if your proxy vote is given to a winner you judge unacceptable would your vote be wasted both quantitatively and qualitatively.

One example of needless qualitative waste is provided by a city council that requires each of its members to be elected only by the voters who reside in one of its districts. Each voter will have only the few candidates running in their district to choose from, rather than all the candidates in the city. This voter is not allowed to help elect a candidate running from another district who they judge to be excellently capable of serving the needs of the city, rather than only the best candidate running from their own district who they judge to be good. Even if this citizen’s vote is perhaps not wasted quantitatively by helping to elect this good candidate, it is at least partially wasted qualitatively by being needlessly excluded from the excellent candidate. An EPR ballot can allow every citizen to grade some or all the candidates in the city, with or without districts.

In fact, needless waste is present in all existing voting methods, whether the method asks voters to rank8, approve9, or score10 as many of the candidates as they might wish. This is because they do not allow any discerning voter fully to express their judgments regarding the suitability of each candidate. The full extent of resulting the qualitative waste is hidden by these systems. Such waste is most pronounced in the method used by most nations where each citizen is only allowed to mark one of the candidates: plurality or first-past-the-post (FPTP) voting as used in the USA, UK, and India.11 All such qualitative waste is also compounded by the fact that these methods can needlessly waste more than 50% of the votes quantitatively when there are more than two candidates for a given office.

Although EPR’s grades provide as much information as possible, we do not deny that the alternative methods provide some useful information.  Yet, assuming that each citizen wants to be accurately and equally represented in the legislative body, EPR maximizes how each citizen’s vote will qualitatively count during the deliberations of their legislative body. At the same time, each citizen’s ballot will proportionately increase the voting power in the legislature of one of the winners.  Only EPR fully satisfies the demand that in the best representative democracy, no citizen’s vote is needlessly wasted, quantitatively or qualitatively.

# Evaluative Voting and the Development of EPR

Until now, none of the available electoral systems could avoid displeasing some voters by wasting their votes. The most recent refinement that has made waste-free voting possible is an adaptation of Balinski and Laraki’s general argument in their book, Majority Judgment (2010/2011 MIT).  For single-winner elections, their method prompts citizens to consider the qualities required by the office being sought.

Accordingly, these authors cogently argue that rather than asking citizens to rank, score, or mark candidates in some other way, they should evaluate (or grade) them. To do this, citizens more comfortably and conveniently grade each candidate’s fitness for office as either Excellent (ideal), Very Good, Good, Acceptable, Poor, or Reject (entirely unsuitable). Again, these grades let voters more discerningly express meaningful and informative choices than those offered by preferences, numeric scores, Xs or ticks.  Grading makes it more likely that the highest quality candidates available will be elected: mayor, governor, president or legislative body.

Each candidate who is not explicitly graded is counted as Reject by that voter. As a result, all candidates have the same number of evaluations but a different set of grades received from the voters. The Majority Judgment (MJ) winner is the one who has received grades from an absolute majority of all the voters that are equal to, or higher than, the highest median grade given to any candidate. This median grade is found as follows:

1. Place all the grades, high to low, top to bottom, in side-by-side columns, with the name of each candidate at the top of each of these columns.
2. The median grade for each candidate is the grade located half-way down each column, in the middle if there is an odd number of voters, or in the lower middle if the number is even.

If more than one candidate has the same highest median grade, the MJ winner is discovered by removing (one-by-one) any grades equal in value to the current highest median grade from each tied candidate’s total until only one of the previously tied candidates currently has the highest remaining median grade.12

In contrast to using ranking, scoring, or approving methods, MJ’s and EPR’s different ways of counting the grades also offer voters fewer incentives and opportunities to vote insincerely or manipulatively.13 Additionally, it is easier to grade a large number of candidates than to rank them. Consequently, MJ and EPR offer citizens every appropriate incentive not only to vote, but to reveal their honest evaluations of each candidate.

We have adapted these MJ features to create EPR for multi-office elections. While MJ must still allow up to 50% minus one of all citizens’ votes to be wasted quantitatively and qualitatively, EPR has the advantage of allowing every citizens’ vote to continue into the legislature through the weighted vote of the winner who at least received their proxy vote.  EPR would enable citizens to elect any legislative body, large or small. For simplicity, our examples only describe how EPR would elect a city council EPR Figurative Illustration.

Again, EPR does not ask citizens to mark only the one candidate they wish to be elected, though their vote will still count even if they only choose to grade one candidate as at least Acceptable.  Alternatively, if a citizen wants their vote to count but feels that they do not yet know any of the candidates well enough to grade them, see how the EPR Sample Ballot, shown below, allows a citizen secretly to write in the code of a Registered Elector who will publicly use their proxy vote to grade the candidates on the citizen’s behalf. In this way, EPR continues exactly to count how many citizens have given their vote directly or indirectly to a member of the legislature. This number becomes the weighted vote that each member will use during the deliberations and decisions made by the legislative body. Each citizen’s vote continues to count proportionately through the vote of this member. Consequently, this method of social choice ensures proportionate representation of each voting citizen, as well as of each self-identifying group of voters, whether minority or majority.

Again, keeping to the principle of one-citizen one-vote, all voters’ evaluations of the candidates can be counted simply but laboriously by anyone who can add and subtract whole numbers. Of course, the available EPR algorithm EPRv2.r completes its count in a few seconds. Exactly how this is done is described in EPR Figurative Illustration and in much greater detail in EPR Count: Detailed Description (also see Supplementary Materials14).

Sample Secret Ballot Paper for EPR, Page 1.

Sample Secret Ballot Paper for EPR, Page 2.

# EPR Summary

In contrast to all existing multi-winner voting systems, EPR explicitly prompts citizens to consider what qualities are ideally required by the office being sought. By allowing citizens comfortably to express the full range of their evaluations of as many of the candidates as they wish, EPR lets voters make more discerning, meaningful, and informative choices than alternative voting methods. This expressiveness of EPR is reflected in the fact that grades cannot be inferred from a list of preferences, while some preferences can be deduced from a voter’s list of grades. Consequently, EPR is more likely to elect the highest quality legislative body available from the point of view of each member of the electorate.

Unlike other methods, the equality that EPR offers to each citizen is exact because only EPR enables each citizen to know that their one vote will continue to count equally both quantitatively and qualitatively and as fully as possible in the legislative body. Such a body most accurately represents the hopes and concerns of the whole electorate. Our simulated election elects the seven members of a city council as shown in EPR Figurative Explanation and Simulated Election Output.13  These seven winners allow up to seven somewhat different sets of hopes and concerns, present in the minds of citizens, to be enthusiastically, skillfully and proportionately represented.

Consequently, an EPR council is more likely to help solve the city’s real economic, social and political problems. This is in part because each EPR council member is more likely to be trusted to negotiate any necessary compromises with opposing members. At the same time, members would be more accountable to their electors because any representative whose behavior failed to match the expectations of their electors could more easily be replaced by one of the larger numbers of attractive candidates who are likely to be available during the next EPR election. This larger number from which EPR voters could choose is a likely result of EPR allowing citizens to grade any or all the candidates running in the whole city, or nation. Also, a larger total number of available candidates could result from the fact that an EPR election would not require districts or an existing type of primary election that needlessly eliminates some attractive candidates.

In contrast to methods that ask voters to rank, score or approve as many candidates as they might want, EPR provides fewer incentives and less scope for citizens to vote dishonestly (manipulatively, strategically, or tactically). This in part is because the EPR citizen knows from the start that their vote will  increase the weighted vote in the legislative body of the winner who either receives their highest grade, highest remaining grade, or proxy vote.   Therefore, EPR voting is easier, and more comfortable, accurate, satisfying, and user-friendly than current methods. Because of this, EPR provides every appropriate democratic incentive for each citizen to vote, to vote honestly, and to be pleased. No citizen’s vote is needlessly wasted, quantitatively or qualitatively.

# References

ANNALS of the Association of American Geographers. Volume 99, 2009 – Pages 184-204,

BALINSKI, M., (February 8, 2008). Fair Majority Voting (or How to Eliminate Gerrymandering). The Mathematical Society of America. Monthly 115.

BALINSKI, M. LARAKI, R. (2010/2011) Majority Judgment, MIT.

BUCKLIN VOTING. ELECTOLOGY, https://www.electology.org/bucklin-voting.

ERDMAN, S. (2010). To Reverse America’s Decline, We Have to Fix Congress’s Dysfunctional Incentives, Center for Collaborative Democracy, 7—17, Appendices III-V,
https://www.olssons.us/thelibrary/Center%20for%20Collaborative%20Democracy_%20Case%20for%20PAR.pdf

ERS97 STV Rules.  http://www.electoralreform.org.uk/votingsystems/stvrules.htm

FAIR VOTE. (https://www.fairvote.org/).

FELSENTHAL, D. S. & MACHOVER, M., ((3/4) 2008). The Majority Judgment Voting Procedure: A Critical Examination. Homo Oeconomicus 25. February 2009). https://pdfs.semanticscholar.org/427e/aa105b46913122c24ad02af2841b7a58c775.pdf

GREEN-ARMYTAGE, J. (2010). Voluntary delegation as the basis for a future political system. http://econ.ucsb.edu/~armytage/proxy2010.pdf

GREEN-ARMYTAGE, J. (2004). A Survey of Basic Voting Methods. http://www.econ.ucsb.edu/~armytage/voting/survey.htm#_ftn12, also see: http://www.econ.ucsb.edu/~armytage/voting/

MARTIN, A. et al. (2019). A new campaign strategy informed by pragmatism: Running on a platform of expanding voting accessibility. Cogent Social Sciences, 5(1), 1631526.  https://doi.org/10.1080/23311886.2019.1631526 ).

MARIJN, M. et al.  19 Oct 2016) Preference votes without preference? Institutional effects on preference voting: an experiment. Journal of Elections, Public Opinion and Parties. Volume 27, 2017 – Issue 2 Pages 172-191, published online.

MEEK, B. (1994). A New Approach to the Single Transferable Vote. Paper I, pp.1-7 and Paper II,pp.8-11. Voting matters, Issue 1, March 1994.  www.votingmatters.org.uk

MILL, J.S. (1861) Representative Government: Utilitarianism; Liberty; Representative Government, Everyman’s Library, 1962, pp.261-8.

MILLER III, J. C. (1969). A Program for Direct and Proxy Voting in the Legislative Process. Public Choice (Fall 1969), pp. 107-113.

SIMMONS, F.  http://www.rangevoting.org/AssetSumm.html.

SUPPLEMENTAL MATERIALS in GitHub:

TULLOCK, G. (1967). Toward a Mathematics of Politics. Ann Arbor. University of Michigan Press, pp. 145-8).

WARF, B. (2008/2009).  The U.S. Electoral College and Spatial Biases in Voter Power.

# Endnotes

1. Stephen Bosworth (stevebosworth@hotmail.com) is a retired Professor of Political Philosophy and Comparative Politics. He taught at universities in the UK, California, and the Turkish Republic of Northern Cyprus. Dr. Anders Corr (corr@canalyt.com) is publisher of the Journal of Political Risk and wrote the original algorithm and simulation with Dr. Bosworth. Stevan Leonard (ngc1432@yahoo.com) is the computer programmer who modified and finalized our EPR algorithm. Contact Dr. Bosworth for more details on EPR, and Stevan Leonard or Dr. Corr for details on the algorithm and computer simulation. This paper is a revision of an earlier version published here: https://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v2/.
2. EPR is new in the sense that it applies the judgments contained in Balinski’s (2010/11) Majority Judgment (MJ) voting to the election of a legislative body, such as a city council or a state’s legislature. The EPR algorithm used to count all the voters’ evaluations of the candidates is also new. Independent of his development of MJ, Balinski (2008) also published a way greatly to improve elections to the U.S. House of Representative:  ‘Fair Majority Voting’. By counting the First-Past-The-Post votes in each of the existing 435 Congressional Districts in a different way, gerrymandering would be neutralized and each Party in the House would be more proportionately represented. However, because it assumed that each Congressperson must have only one vote in the House, unlike EPR, FMV would still needlessly waste some citizens’ votes both quantitatively and qualitatively.
3. Accordingly, we also agree with A. Martin, et al.’s recommendation (2019) that candidates should energetically campaign for additional pragmatic measures to enable all citizens to participate in elections. However, unlike our EPR article, these authors do not attempt to compare the different ways these voting methods do or do not prompt more citizen participation by allowing their votes fully to count both quantitatively and qualitatively.
4. Balinsk and Laraki convincingly argue that the common language provided by these six grades is more expressive and meaningful than the relatively impoverished languages used by any of the existing methods (pp. 169, 171, 283, 306, 310, & 389). B&L also see their argument as supported by G.A. Miller.Correctly, B&L report that Miller also provides evidence that while a ‘greater number of grades permit a finer distinction … [they also demand] a higher degree of expertise and discernment’.  An ‘experienced professor who has … evaluated some thousands of students … has a well-developed set of benchmarks that together define absolute evaluations that dominate the relative comparisons.  …. The same is true of voters:  They have seen and learned about able statesmen—presidents and prime ministers of countries, mayors of cities, senators, representatives—as well as inept or corrupt officeholders.  [Similarly, they] … have clear benchmarks.’  B&L accept that in the light of more tests and uses, some improvements to their six-level scale might be developed.  Such intellectual creations must always remain a work in progress.    I see their choice of six as resulting from their concern to offer a scale that would comfortably be a part of the common evaluative language of the whole electorate.

In contrast, the existing methods only allow citizens to vote in a single-winner election by:

1. putting an X in the box next to the one candidate you want to be elected (‘plurality’ or ‘First-Past-The Post’ (FPTP), the candidate receiving the largest number of Xs wins,
2. putting an X in the box next to each candidate you believe would be an acceptable winner (APPROVAL), the candidate who receives the largest number of approvals wins,
3. giving a number score (e.g. 1-10) to any number of the candidates (SCORE or RANGE), the candidate who receives the largest total wins, or
4. ranking the candidates you like in order of your preferences (Instant Run-off Voting (IRV – also called Rank Choice Voting (RCV), and all the Condorcet methods).

Logically, a citizen’s expected FPTP, APPROVAL, SCORE, or ranking vote for a particular election can sometimes be inferred from the grades they have actually given.  However, if the election instead requires a citizen to use only any one of these other methods, no observer could infer which grade or grades that citizen must logically give in their place.  This is another way of showing that MJ’s and EPR’s six grades provide a richer common language by which citizens can most comfortably and meaningfully express their judgments about the suitability of each candidate for office.  Grades provide the most information.

At the same time, we consider the second-best method would be the one that asks voters to rank only the candidates they judge acceptable.  They can give more than one candidate the same level of preference.  No more than seven levels of preference must be used.  Some of the rankings given using this second-best method would only allow an observer plausibly to suggest (not infer) what grade or grades a given ranking might be given instead.

If this type of ranking were used to elect multi-winners, we could refer to it as a modified version of Single Transferrable Voting (STV).  To be second best to EPR, its rankings would also have to be counted in the way most similar to EPR’s counts of grades.  Consequently, each STV voter could guarantee that one of the elected members of the legislature receives either their first preference, remaining highest preference, or proxy vote.  Like EPR, exact quantitative proportionality would be assured.  Still, only EPR offers the extra benefit of revealing all the qualitative judgments of the electorate regarding the suitability for office of each candidate and winner.

Again, we see MJ and EPR as the best methods because they prompt citizens to use an expressive and comfortable common language for grading the candidates from Excellent to Reject.  The meaning of grades are more readily understood than rankings or numbers. Most voters would find it easier give 20 or more candidates one of 6 to 8 grades rather than to give each candidate a different number or ranking.

We already know that each civilization, society, community, state, or nation continues to develop such evaluative languages.  These languages allow persons comfortably to express their judgments of people regarding different levels of merit.  For example, students in the USA commonly receive a graded of A, A-, B+, B, B-, C+, C, C-, D, or F for their performances.  Denmark gives 00 to the worst and 13 to the best performances.  France uses a 0—20 scale:  10 -11 ‘adequate’, 12 -13 ‘passable’; 14-15 ‘good’; 16 ‘excellent; 17 ‘outstanding’; 18-19 ‘nearly perfect’; 20 is perfect.   These are ‘intellectual creations. ’ These grades ‘are usually given very careful definitions.’  Each level becomes more meaningful and precise with the passage of time and use.   These levels have ‘no meaning other than what is ascribed to them by their users.’ (Balinski (2010/2011), pp.166-169).

In November 2009, majority judgment was officially used by the Nieman Foundation of Harvard University to discern the Louis Lyons Award for Conscience and Integrity in Journalism….  The jury was composed of 19 Nieman Fellows.  Five journalists … were the nominees.  All of them were very highly considered.  As a consequence, the … Fellows chose the following common language of seven grades:  Absolutely Outstanding, Outstanding, Excellent, Very Strong, Commendable, and Neutral.  The winner’s majority-grade was Absolutely Outstanding, two nominees’ majority-grades were Outstanding,  and two were Excellent.  Five of the 19 judges gave their highest grade to more than one nominee; three gave no Absolutely Outstanding; Outstanding was the lowest grade assigned by five; and exactly one judge gave different grades to all candidates (so only one ranked all candidates). This confirms the qualitative behavior of the voters in the Orsay experiment (Balinski (2011) p.390).

Marijn, A. et al.(2016) report some evidence that seems to support our assumption that many voters will gladly take advantage of the additionally expres sive choices offered by EPR to grade as many candidates as they might wish. This seems to follow from their experiment to test the extent to which different panels of voters from the Netherlands and Belgium might choose to use some different features of their respective Party-List voting systems.  The Belgian system allows voters to rank all of the candidates on the Party list they have selected.  In contrast, the Dutch system requires voters to select only one candidate on their Party’s list.  When given the option, a number of Dutch voters ‘actively’ chose to rank the candidates instead.

1. The three ways proxy votes are used by EPR are varieties of ‘asset voting. ’Gordon Tullock included weighted votes in his own proposals. However, in Tullock’s case, these would have only been produced by using the existing FPTP or Plurality arrangements in the USA. Sol Erdman’s Personal Accountability Representation (PAR) proposals also include weighted votes that are to be discovered by using modified STV. Unlike EPR, the weighted votes proposed by Erdman are not derived by allowing citizens to evaluate as many candidates in the whole country as they might wish. Instead, his PAR limits each voter to ranking only the candidates who are seeking to represent the larger geographically defined electoral district in which they reside. Each such district is still much smaller than the whole state or nation.
2. When the super-popular candidate has received fewer or the exact number of ballots required to be transferred as extras, and when these ballots also award a remaining highest grade to one of the other eligible candidates, each of these ballots is transferred.  However, when the number of these ballots exceeds the number that must be transferred, the ones to be transferred are determined by lot. These rules are more comprehensively described and illustrated in the Supplementary Materials.14
3. Note that the sample EPR ballot allows any citizen, if they want, explicitly to prohibit any proxy vote to be given on their behalf.
4. With ordinary IRV, voters are asked to rank the candidates 1, 2, 3, etc. If no candidate receives first choices from at least 50% plus one of all the voters, the candidate who has received the fewest number of first choices is eliminated. The votes of the citizens who had given their first choice to this eliminated candidate are now given to their respective second choice candidates (if any). This process is repeated until one of the remaining candidates has received a majority of the remaining active ballots.

Different varieties of this method have been used for many years in the Republic of Ireland, Malta, and Australia.  In the USA, Maine has recently adopted it and a number of cities use it including San Francisco.  Currently, using the names Rank Choice Voting (RCV) or Choice Voting, IRV is being skillfully and energetically promote in the USA by FairVote (https://www.fairvote.org/).

IRV’s voting language is impoverished when compared with that of MJ and EPR.  However, it is richer than those used by FPTP, APPROVAL, or SCORE.    At the same time, ordinary IRV and STV have the flaw of not guaranteeing the election of a winner who receives most of the preferences, let alone a majority of all the ballots cast.  This is illustrated by the following example in which the candidate preferred by the largest number is not elected but eliminated:

Example: If 100 citizens vote in the following way, IRV would make candidate C win. B would be eliminated even though that candidate is preferred by more citizens: 20 citizens’ first choice votes and by 80 citizens’ second choice votes. Candidate C is supported only by 40 first choice votes and by 20 second choice votes. Candidate A is supported only by a different group of 40 first choice votes. Still IRV elects C in this example.

100 CITIZENS:

40 prefer A over B over D

40 prefer C over B

20 prefer B over C

When C is elected, also notice that all votes cast by the 40 voters (who preferred A over B over D) are wasted both quantitatively and qualitatively in the senses defined in the Votes Wasted Quantitatively and Qualitatively section of this article.  Also, the 20 votes that eventually were added to C’s victory were wasted qualitatively in part.

Instead, Majority Judgment (MJ) guarantees that the winner will be the candidate who is graded most highly by at least 50% plus one vote of all the votes cast,  the candidate seen by the electorate as the one most qualified for office.  From the perspective of MJ, we might ask the 40 voters in the above example who gave their first choice to A, what grade they would give to that candidate.  Again, we would have to ask them because we cannot infer grades from preferences.

Single-winner Condorcet ranking methods also seek to discover the candidate who is preferred by the largest number of voters when compared with each other candidate in turn. However, one trouble is that there is not always such a winner. Unlike Majority Judgment (MJ), two or more Condorcet candidates may be tied, neither with an absolute majority. Ties must be broken in ways that are somewhat arbitrary. Nor is it ever discovered whether the winner is also the one most highly regarded by the voters who were counted as having preferred this winner. This last flaw stems from the fact that, unlike both IRV, STV, MJ and EPR, no Condorcet count takes notice of the different intensities with which each candidate is or is not preferred over each of the other candidates. This is true even though each citizen’s completed ballot does provide some of this information. Similar flaws remain when any Condorcet method is used to elect multi-winners. The Condorcet counts are too complex for many ordinary citizens fully to understand.

1. Approval voting asks citizens expressly to approve or disapprove of as many of the candidates as they might wish. The candidate with the most approvals wins. In contrast to MJ and EPR, APPROVAL does not allow voters to express the different intensities with which they approve, disapprove, or value each candidate. Nor does it guarantee that the winner will have received approvals from at least 50% plus one of all the voters. It also prompts more strategic voting than does either MJ or EPR.
2. Typically, using the SCORE voting method for a single-winner contest asks citizens to give a score of 0 to 9 for each of as many of the candidates as they might wish. The winner is the candidate who receives the highest total or average score. If every candidate who is not expressly scored by a voter is counted as having received a 0 from that voter, this prevents the following type of candidate from winning: a candidate who is expressly scored most highly, but only by a few voters. However, unlike EPR, this rule still allows the principle of one-citizen one-vote to be violated by SCORE voting. This is because the high score from one citizen has more weight than any low score from another citizen. Especially in contrast to EPR (and MJ), this reality prompts more voters to score candidates strategically, rather than honestly. However, this difference would be somewhat reduced if the SCORE winner was instead the candidate who had received the highest median score (not the one with the highest average). This change to SCORE voting would make it closer to MJ, especially if scores were limited from 1 to 6. This version of SCORE would still not allow discerning voters most meaningfully and clearly to express their judgments about the suitability of each candidate for office. Numbers are less informative and stable than the grades.
3. Warf (2008) provides a dramatic example of the inequality and wasting of votes in the U.S.A. Warf’s sophisticated mathematical analysis concludes that the relative ‘voter power [of each citizen in the U.S. when electing the President] is highly contingent, ephemeral, transitory, and unpredictable’. The ‘Relative voter power [of each citizen] can vary widely in time and space, ranging from a low [score] of 0.08 in Alabama in 1960 to a high [score] of 20.2 during the highly visible and very close race for Florida in the 2000 election … [in] which George W. Bush won by the extremely slender margin of 537 votes ….’  Such ‘contingent and unpredictable’ inequality and waste would be entirely removed if the first stage of the election of the President were instead conducted in the 50 states by using EPR.  MJ would then be used In the second stage of the count to combine all these separate ballots from each of the 50 states.  Thus, each citizen’s vote would always equally count as one.  Also, each president would be elected by at least 50% plus one of all American voters.
4. Balinski, pp. 5, 17. It might be suggested instead that the widest possible majority support for the single winner would be found by electing the tied candidate who had received the largest number of grades equal to or higher than the highest median-grade initially received by any of the candidates. This modification of MJ could be called MJ+.
5. Balinski, pp. 14, 15, 19, 187-198, 374. In contrast to other systems, B&L show how MJ cuts by almost half any scope or incentive offered by other methods to vote dishonestly.
6. Supplementary Materials in GitHub: