[EM] (3) MJ -- The easiest method to 'tolerate'

[Toby Pereira]

There are of course many different types of election, and while people may argue that online voting is not suitable for national parliamentary elections, it's likely to work for certain "lesser" elections.

And as I have argued on the CES Google Group, if you have online voting, you can have the live provisional result displayed publicly, and allow people to change their vote up until the deadline. With this in place, normal score voting should work perfectly well and allow people to adopt reasonable strategy without having to guess in advance what other people will do. Any other system (other than approval voting) is likely to be too complex or difficult to work with for this.

But you might have to have a period where the election ends non-deterministically to stop voters engaging in weird and unpredictable behaviour by adding or removing support for candidates immediately before the deadline.


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On Mon, 5/9/16, Jameson Quinn <jameson.quinn at gmail.com> wrote:

 Subject: Re: [EM] (3) MJ -- The easiest method to 'tolerate'
 To: "steve bosworth" <stevebosworth at hotmail.com>
 Cc: "election-methods at lists.electorama.com" <election-methods at lists.electorama.com>, "stepjak at yahoo.fr" <stepjak at yahoo.fr>
 Date: Monday, 5 September, 2016, 21:30
 
 It's
 really hard to respond point-by-point as a third party in a
 discussion like this. However, I'd like to say in
 general that I believe that Majority Judgment, and
 more-generally, the class of "median" or
 "graded Bucklin" systems which includes MJ, MCA,
 GMJ, ERB, DA, etc., are the best non-delegated single-winner
 systems for a potentially-strategic electorate, in terms of
 outcome. 
 (I'll include
 a glossary at bottom. All of these systems are basically
 similar in that candidates are graded independently into
 grade classes and the winner is one of those with the
 highest median. Until I get there, I'll just use
 "MJ" as a representative stand-in for an arbitrary
 member of this class of systems.) 
 Why do I believe this? Because I
 think these systems would allow a large supermajority of
 voters to vote "unstrategically" in a large
 supermajority of elections. That is, they could arrive at a
 iterated-strategically-optimal ballot by simply comparing
 each of the candidates to some universal scale which was
 calibrated using simple summary statistics of historical
 data about elections for the same office (or, if no such
 historical data is available, using polling and/or
 historical data for comparable elections).
 In order to argue the above, I think
 it will work best to refute the objections commonly raised
 against MJ.
 First,
 there is the failure of the later-no-harm (LNH) criterion.
 But note: MJ actually does pass a weaker version of LNH:
 rating additional candidates at above bottom will not harm
 the winner as long as those candidates are ranked below the
 winning median. My claim is that over time, the winning
 median grade will mostly fall in a given band of grades; for
 instance, using letter grades, between B- and D+. In that
 case, making distinctions between A and B at the top or D
 and F at the bottom are strategically safe. 
 Even the rare cases where the
 winning median might be outside this band, it is unlikely
 that an honest ballot will violate LNH in practice. Consider
 the possibilities. If the winner has an unusually high
 median, they are an unusually good candidate, and it is
 unlikely that any strategic voting by their opponents would
 be enough to unseat them. (And that's a good thing). If
 the winner has an unusually low median, that is usually an
 indicator that the electorate is unusually fragmented into 3
 or more distinct factions. If those factions can be located
 along a 1D spectrum, then the voters who might cast
 strategically non-optimal votes are the centrists, whose
 favored candidate is probably the honest Condorcet winner.
 But centrists are likely to honestly view both extremes as
 equally bad, and thus to honestly vote both at
 F. 
 Thus, the chances
 of an arbitrary ballot being non-optimal are product of the
 minority fraction of elections with such extreme division,
 multiplied by the minority fraction of the electorate who
 are centrists, multiplied by the minority fraction of
 centrists who would honestly rate a given non-centrist
 winner above F. I'd argue that each of these fractions
 are almost certain to be below 1/3, making the overall
 "zero-information strategic incentive" equal to
 1/27 times the possible advantage from a strategic ballot.
 If that last factor is, say, 2/3 of the distance between the
 optimal and the pessimal candidate, the overall ZISI is
 around 2.5% of that distance. As a statistician, I have a
 name I'd use for that kind of number in most contexts:
 "insignificant".
 A similar argument can be used
 against the charge that MJ can elect a Condorcet loser (or
 even a majority loser in a two-way election). Any such
 scenario where this happens involves at least two critical
 portions of the electorate badly misjudging what the likely
 winning median will be, and doing so in opposite directions.
 Note that the winning median is much easier to roughly guess
 ahead of time than the specific winner or frontrunners;
 guessing the former can be done using historical data,
 while, in the absence of two-party domination, the latter
 probably takes current polling data, likely to be harder to
 come by. But even if people guess the winning median
 poorly... how likely is it that there will be significant
 fractions misjudging in both directions in favor of a given
 Condorcet loser, while none misjudge the median against that
 candidate?
 ...
 To me, the toughest realistic
 election scenario is the chicken dilemma. For instance,
 consider the following 900-voter scenario300:
 A>B>>C200:
 B>>A>C400: C>>B>A
 (where ">>"
 indicates universal agreement, and ">" at
 bottom indicates 90% agreement and 10%
 reversal)
 The
 "correct" winner here is pretty clearly B;
 they'll win an honest election under Condorcet, score,
 or MJ. How would this play out in different systems?
 I'll distinguish "first time", with a mix of
 honesty and naive strategy, and "later", with
 something approaching evolutionarily stable
 strategy.
 In
 plurality, C would win the first time. Eventually, the A and
 B factions would manage to coordinate strategy, probably
 electing A in the long term. That sub-optimal result would
 then mean that B voters would be more-or-less permanently
 disenfranchised.
 In
 IRV, A would win the first time, leaving the C voters very
 unhappy. If enough of them were ready to strategically
 compromise, they might be able to elect B; but I think
 that's unlikely. More likely, they'd just complain
 until IRV was reverted to plurality, as happened in
 Burlington.
 In Borda
 with truncation, C would win the first time, then later A,
 as in plurality. Eventually that might transition to a win
 for B as the C voters stopped truncating.
 In approval, B would probably win
 the first time and stably going forward. However, if naive
 strategy was too uncompromising, or if later strategy was
 too inclined towards brinksmanship, either of the other two
 might win occasionally.
 In score, B would win the first
 time, and then later it would come to behave as approval;
 that is, B with a risk of brinksmanship
 pathologies.
 In MJ, B
 would win the first time and stably going forward. It would
 take extreme brinksmanship for C to win; frankly, I find
 that implausible. A might win occasionally, motivating the C
 voters to rate B above zero in the long term.
 (The only system I know of that
 would be more certain to elect B than MJ would be
 SODA.)
 ...
 As promised, here's my glossary
 of graded Bucklin systems:
 ERB: Equal Ratings Bucklin.
 "Equal ratings" just means that ballots are
 graded, not forced to be strict rankings. 4 or more grade
 levels, highest median, tiebreaker is number of votes at or
 above median.MCA: Majority Choice Approval. As
 above, but 3 grade levels (preferred, approved,
 unapproved)GMJ: Graduated Majority Judgment. 4 or
 more grade levels, highest median, tiebreaker is average
 between number of votes at or above median and number of
 votes above median.DA: "Double
 Approval" or "Disqualify/Approve" voting.
 Voters can rate each candidate preferred, neutral, or
 disqualified. (Both preferred and disqualified is also legal
 and counted, though it's strategically nonsensical.)
 Winner is the most-preferred among those not majority
 disqualified. If all candidates are majority-disqualified,
 winner is simply most-preferred. Any candidate who is
 majority-disqualified is prohibited from appearing on the
 ballot for the same office in the following election.
 
 Lately,
 I favor DA, as being the simplest to explain and the most
 intuitive to reason about for most people. I expect that the
 majority of voters would prefer a single candidate, and use
 a rough approval strategy for disqualification (that is,
 disqualify one frontrunner and anybody worse.) The good
 thing is that cooperation is stable in DA in an iterated
 chicken dilemma scenario; the prospect of tit for tat
 retaliation is enough to discourage brinksmanship
 strategy.