[EM] “goal of a better election method”

[steve bosworth]

Re: “goal of a better election method”

To all (but prompted by Sennet Williams and Rober Bristow-Johnson, and earlier by Michael Ossipoff, Richard Fobes, Kristofer Munsterhjelm,  Steve Eppley, Jameson Quinn, and Kevin Venzke)

Since January 9th (Election-Methods Digest, Vol 151, Issue 12) there have been several answers to Sennet Williams’ question: “What is the goal of a "better" election method?”  Please correct me if I am mistaken but the answer that I would like to suggest below would effectively satisfy the answers given by, e.g. Robert Bristow-Johnson’s:  “The end goal of a "better" election method … is FAIRNESS and INCLUSION.  Fairness for voters means
1. Level playing field
for *all* voters ("One person, one vote")
2. No burden of tactical voting (therefore no punishment for voting sincerely) in a multi-candidate election. ?No voter regret.?
3. …. 10 ….”

My suggested goal for a single-winner election (e.g. for a president, governor, or major) is Balinski and Laraki’s:

“The purpose of … an election is to select, if possible, some candidate who shall, in the opinion of a majority of the electors, be most fit for the post…” (E. J. Nanson, quoted by Balinski and Laraki, Majority Judgment, MIT, 2011, p.209).

Also, “to gather as precisely as possible, the true opinions and evaluations of individuals, and to determine as precisely as possible, the true aggregate wills of electorates ….” (Ibid, p. 388).

Accordingly, I also seem to be coming to the conclusion that a refined improvement on Balinski and Laraki’s Majority Judgment (MJ) method called Highest Majority Judgment (HMJ) by me would be the most efficient way of electing this “most fit” candidate.  As will be explained below, HMJ guarantees that the winner will be the candidate most valued for the job by at least an absolute majority of all the voters, i.e. the candidate believed on average by at least an absolute majority to be the most qualified for the office.  Thus, HMJ also seems to be the “easiest single-winner voting method to tolerate”. Please explain any mistakes I might be making if I see HMJ as superior to the other good methods, e.g. any known variant of Immediate Run-Off Voting (IRV), SCORE (Range), Maximized Affirmed Majorities (MAM), or APPROVAL.

Firstly, I believe that Balinski and Laraki  explain how MJ avoids both “Condorcet paradox” and the “Arrow paradox” (ibid, pp.182-3).  Secondly, I believe that B&L “prove” (pp. 15, 19, 186-198) that MJ provides only about “half” the incentives or opportunities for anti-democratic “strategic” voting to be successful. If you disagree, please explain the flaw in their argument. Until I see such a flaw, MJ would seem to offer no reason for a savvy voter to expect to have a probable “strategic” advantage over less savvy voters, i.e. if and when they might choose to misuse MJ’s ballot, in effect, to “rank” rather than to “grade” the candidates.  If B&L’s proof is valid (and it is also true for HMJ), it, more than the above methods, largely frees voters from the burden of perhaps having to dishonestly ‘grade’ some of the candidates. This is because with HMJ, it is probable that their honest ‘grades’ will do all they can to help elect the best candidate in their view.  This is why Balinski and Laraki say that voting “honestly” with MJ is likely to be the “dominant strategy” (pp.190).  Unfortunately, IRV, SCORE, MAM, and APPROVAL sometimes truly offer some very complicated reasons for very savvy citizens to vote dishonestly while hoping to make the election of their most preferred candidate more likely. By largely removing this burden, HMJ would seem to help to minimize such distortions to the democratic process, i.e. to make the election of the best candidate as likely as possible.

I will now explain in more detail how HMJ works:

  1.  Uniquely, HMJ (and MJ) asks each voter simply to record their “evaluation” of each candidate by giving each candidate one of the following “grades” depending on how closely each candidate comes to fitting the citizen’s own image of an “excellent” candidate: EXCELLENT (5), VERY GOOD (4), GOOD (3), ACCEPTABLE (2), POOR (1), or REJECT (0) – each blank is interpreted as REJECT.   Such grades are likely to be meaningful at least to any person who has gone to school.  It is easier to grade many candidates than to rank them.  Every citizens’ “grade” for every candidate continues to be part of the count until the absolute majority winner is discovered.

  2.  Each candidate receives the same number of “grades”.  To begin the count, all of each candidate’s “grades” are listed from highest to lowest, left to right.  Next, each candidate’s “median-grade” is identified (i.e. the middle one on the right if there is an even number of voters).

  3.  The HMJ winner is the candidate discovered to have the highest average of all the grades she has receive to the left of her “median-grade” and including her “median-grade”.  If there is more than one candidate with this same highest average grade, each is a potential winner (see Example 1 below).  In this event, HMJ discovers the winner by comparing, one by one, the next grade that each has received immediately to the right of their respective medians.  The winner is the first candidate in this sequential comparison discovered to have a next grade higher than any of the other previously tied potential winners (see Example 2 below).

Example 1:

Y wins with HMJ, but X wins with MJ & Bucklin MJ

X:  VGGPP or 43311………..10/3 = 3.66

Y:  EEAAP or 55221 …………12/3 = 4

Example 2:

X wins with MJ & BMJ, but with HMJ, X & Y are initially tied.  However, by comparing the grades to the right of the median, Y is discovered to be the HMJ winner.

X:  EVGPP or 54311………..12/3 = 4; 13/4 = 3.33

Y:  EEAAA or 55222…………12/3 = 4; 14/4 = 3.66

In this way, HMJ guarantees that the winner will be the candidate most highly valued by at least an absolute majority of the electorate.

While Balinski and Laraki clearly explain their own methods for breaking MJ ties, I see their methods to be much more laborious and less efficient than HMJ’s.  Firstly, MJ identifies all the candidates who have received the “highest majority-grade”.  If there is more than one such candidate, MJ’s simplest tie breaking process uses “majority-guages” (pp.9ff).  This differs from HMJ’s by simply comparing each such candidate’s number of grades listed to the left and to the right of all the grades each such candidate has received which are the same as their common “highest median-grade”.  If and when this comparison fails to discover a winner, then the “majority-values” (pp. 6ff) of the tied candidates are compared instead.  This is done by sequentially discovery and listing each tied candidate’s new “median-grade” upon the removal of the current median-grade from the total list of all the grades each such candidate had initially received.  This is repeated until one of these candidates is found to have the highest new median-grade.  Thus, unlike HMJ, MJ does not average the variety of different degrees of “evaluation” listed to the left of each candidate’s “median-grade”, i.e. the grades that may be distributed differently among this group of grades received by each of the tied candidates.

Therefore, in contrast to the above rival methods, HMJ

  1.  offers the greatest encouragement for each citizen to vote;

  2.  allows and most strongly encourages (with MJ) each citizen most fully, exactly and honestly to express their different “evaluations” of each candidate;

  3.  again, (with MJ) offers only about “half” the incentives or opportunities for anti-democratic “strategic” voting to be successful. Thus, B&L argue that for most citizens, “sincere voting” will be the “dominant strategy” (pp. 190); and

  4.  has the virtue (with MJ) of not requiring any arbitrary procedure to discover the absolute majority winner among any initially tied candidates unless every voter has “graded” each candidate identically.

Also, I note that in contrast to HMJ:

  1.  IRV can eliminate some candidates before the winner is discovered.  Unfortunately, one of these eliminated candidates might be the one who is preferred by more voters than any other candidate.  This is true even though IRV also guarantees that its winner will have been explicitly preferred by a majority over all the remaining candidates;

  2.  SCORE’s winner has not necessarily received ratings higher than 0 from a majority of the voters.  Its number ratings of candidates are less meaningful than “grades”.   Also, especially if its highest rating is more than “7”, they would also be less “discerning” (Ibid, p.283) than the 6 different “grades” used by HMJ.  This is because empirical studies have discovered that most people cannot meaningfully distinguish between more than seven “grades” of valued human behavior;

  3.  MAM’s aggregation of all the voter’s preferences ignores some of the different ordinal preferences recorded on each voter’s ballot.  In contrast, all the different degrees of evaluation of all voters used by HMJ (i.e. “grades”) contribute to the discovery of its absolute majority winner.  Also, many ordinary voters would find it much harder to understand how their MAM preferences are aggregated in an attempt to find the Condorcet winner (or the one produced by its tie breaking procedure). Finally, an MAM winner may not have been explicitly preferred by a majority of the voters;

  4.  APPROVAL does not allow citizens to express the full range of different degrees of “approval” that voters may feel with regard to the available candidates.  Consequently, a voter’s marking of the candidates she only weakly favors may help to defeat the candidate she most enthusiastically favors.  Also, the APPROVAL winner may not have been “approved” by a majority of the voters.

I look forward to your feedback.

Steve

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