[EM] [CES #15135] Renaming SARA to "majority score"
Jameson Quinn
jameson.quinn at gmail.com
Thu Oct 27 20:47:49 PDT 2016
2016-10-27 20:37 GMT-04:00 Andy Jennings <elections at jenningsstory.com>:
> Jameson,
>
> Wouldn't it be possible to abuse rule 2 to cause chaos?
>
> For example, I change someone from "accept" to "reject", which would
> trigger his elimination. But if he is the last candidate with over 50
> points, that triggers rule 2 to be skipped entirely, resurrecting (him and)
> one or more other candidates, which changes the winner. IIA violation?
>
No. You lower X from accept to reject; X was the only non-eliminated
candidate over 50 points, so X was the winner. So, by lowering X, you
change the winner from X to not-X. That's perfectly monotonic; nothing
wrong with that.
(It might be that you actually preferred X over not-X. In which case you
should have voted X above not-X if you really cared about that distinction.
Since you failed to do so, you can't really complain.)
> On Thu, Oct 27, 2016 at 11:27 AM, Jameson Quinn <jameson.quinn at gmail.com>
> wrote:
>
>> I'm renaming the system I'd called SARA to "majority score voting
>> <http://wiki.electorama.com/wiki/Majority_score_voting>". The SARA
>> acronym is nice, but it relies on putting the rating categories out of
>> their natural order (which would be the much-uglier "SAAR").
>>
>> I've also renamed some of the rating categories; they are now "support,
>> assist, accept, reject" with a default of "accept". I believe that these
>> words give a better intuitive sense of what each rating does.
>>
>> I've done some significant work on the wiki page. In particular, I showed
>> criteria compliances. I also went through minor spoiler, chicken dilemma,
>> and center squeeze scenarios, showing both honest results and probable
>> tactics. One important note is that chicken dilemma truncation tactics will
>> definitely backfire for a subfaction that's smaller than 25% if there's any
>> subfaction that's larger than 25% (which must be the case in a two-way CD).
>> Since, given reasonable margins of error for polling, there will very
>> rarely be a smaller CD faction which can be confident that it's over 25%,
>> this is yet another reason that CD issues will never get off the ground in
>> this system.
>>
>> For instance, let's say that the total error (both statistical and
>> structural) of polls is about 4%, and that a faction will not attempt CD
>> strategy unless it believes itself to be the smaller faction but over 25%.
>> That would mean that the smaller faction would have to be 29% and the
>> larger one 33%; leaving just 38% for the minority threat faction. That's an
>> awfully tight window for the scenario to work; given polling fluctuations,
>> it would be very unlikely that a scenario would be stably inside this
>> window for long enough for the faction to plan and execute a CD betrayal.
>>
>> Here's the wiki page as it currently stands:
>>
>> Majority score voting
>> <http://wiki.electorama.com/wiki/Majority_score_voting#mw-head>
>> <http://wiki.electorama.com/wiki/Majority_score_voting#p-search>
>>
>> Majority score voting chooses the candidate with highest score among the
>> serious candidates who aren't rejected by a majority. Step by step, it
>> works as follows:
>>
>> 1. *Voters can support, assist, accept, or reject each candidate.
>> Default is accept. Candidates get 2 points for each percent of "support"
>> and 1 point for each percent of "assist", for a total of 0-200 points.*
>> - *Obviously, you should support the best candidates (perhaps a
>> quarter of them), and reject the worst (perhaps half of them). For the
>> rest, the candidates who are between average and good, a simple rule of
>> thumb is to assist when you're afraid of somebody worse, and accept when
>> you are hoping for somebody better.*
>> 2. *Eliminate any candidates rejected by over 50%, unless that leaves
>> no candidates with over 50 points.*
>> - *If possible, the winner shouldn't be somebody opposed by a
>> majority. But this shouldn't end up defaulting to a candidate who couldn't
>> at least get accepted by over 1/2 or supported by over 1/4.*
>> 3. *Highest points wins. In case of a tie, fewest rejections wins.*
>> - *This finds the candidate with the widest and deepest support.*
>>
>> Note: Majority score voting was originally called SARA voting, an acronym
>> for the 4 ratings voters can give. However, putting these ratings
>> out-of-order is confusing, even if it results in a nice-sounding acronym.
>> Contents [hide <http://wiki.electorama.com/wiki/Majority_score_voting#>]
>>
>> - 1Criteria compliance
>> <http://wiki.electorama.com/wiki/Majority_score_voting#Criteria_compliance>
>> - 2An example
>> <http://wiki.electorama.com/wiki/Majority_score_voting#An_example>
>> - 3Other scenarios explored
>> <http://wiki.electorama.com/wiki/Majority_score_voting#Other_scenarios_explored>
>> - 3.1Worst case?
>> <http://wiki.electorama.com/wiki/Majority_score_voting#Worst_case.3F>
>> - 4As the first round of a two-round system ("majority score with
>> runoff")
>> <http://wiki.electorama.com/wiki/Majority_score_voting#As_the_first_round_of_a_two-round_system_.28.22majority_score_with_runoff.22.29>
>> - 5Relationship to NOTA
>> <http://wiki.electorama.com/wiki/Majority_score_voting#Relationship_to_NOTA>
>>
>> Criteria compliance[edit
>> <http://wiki.electorama.com/w/index.php?title=Majority_score_voting&action=edit§ion=1>
>> ]
>>
>> Majority score passes the favorite betrayal criterion
>> <http://wiki.electorama.com/wiki/Favorite_betrayal_criterion>, the majority
>> criterion <http://wiki.electorama.com/wiki/Majority_criterion>, Independence
>> of irrelevant alternatives
>> <http://wiki.electorama.com/wiki/Independence_of_irrelevant_alternatives>
>> , Local independence of irrelevant alternatives
>> <http://wiki.electorama.com/wiki/Local_independence_of_irrelevant_alternatives>(under
>> the assumption of fixed "honest" ratings for each voter for each
>> candidate), Independence of clone alternatives
>> <http://wiki.electorama.com/wiki/Independence_of_clone_alternatives>,
>> Monotonicity <http://wiki.electorama.com/wiki/Monotonicity>, polytime
>> <http://wiki.electorama.com/w/index.php?title=Polytime&action=edit&redlink=1>
>> , resolvability
>> <http://wiki.electorama.com/w/index.php?title=Resolvability&action=edit&redlink=1>,
>> O(N) summability
>> <http://wiki.electorama.com/w/index.php?title=Summability&action=edit&redlink=1>,
>> and the later-no-help criterion
>> <http://wiki.electorama.com/wiki/Later-no-help_criterion>.
>>
>> There are a few criteria for which it does not pass as such, but where it
>> passes related but weaker criteria. These include:
>>
>> - It fails the mutual majority criterion
>> <http://wiki.electorama.com/wiki/Mutual_majority_criterion>, but
>> passes if the mutual majority in question unanimously rejects all
>> candidates outside their mutually-preferred set. It also passes if the
>> number who give the strongest candidate in the set a rating below "support"
>> is less than three times the amount by which the overall group exceeds 50%.
>>
>>
>> - It fails the Condorcet criterion
>> <http://wiki.electorama.com/wiki/Condorcet_criterion>, but for any
>> set of voters such that an honest majority Condorcet winner exists, there
>> always exists a strong equilibrium set of strictly semi-honest majority
>> score ballots that elects that CW.
>>
>>
>> - It fails the participation criterion
>> <http://wiki.electorama.com/wiki/Participation_criterion> but passes
>> the semi-honest participation criterion
>> <http://wiki.electorama.com/wiki/Semi-honest_participation_criterion>.
>>
>> It fails the consistency criterion
>> <http://wiki.electorama.com/wiki/Consistency_criterion>, the Condorcet
>> loser criterion
>> <http://wiki.electorama.com/wiki/Condorcet_loser_criterion>,
>> reversibility <http://wiki.electorama.com/wiki/Reversibility>, the majority
>> loser criterion
>> <http://wiki.electorama.com/wiki/Majority_loser_criterion>, and the later-no-harm
>> criterion <http://wiki.electorama.com/wiki/Later-no-harm_criterion>.
>> An example[edit
>> <http://wiki.electorama.com/w/index.php?title=Majority_score_voting&action=edit§ion=2>
>> ]
>> Error creating thumbnail: File missing
>>
>> Imagine that Tennessee is having an election on the location of its
>> capital. The population of Tennessee is concentrated around its four major
>> cities, which are spread throughout the state. For this example, suppose
>> that the entire electorate <http://wiki.electorama.com/wiki/Electorate> lives
>> in these four cities, and that everyone wants to live as near the capital
>> as possible.
>>
>> The candidates for the capital are:
>>
>> - Memphis <http://en.wikipedia.org/wiki/Memphis> on Wikipedia, the
>> state's largest city, with 42% of the voters, but located far from the
>> other cities
>> - Nashville <http://en.wikipedia.org/wiki/Nashville> on Wikipedia,
>> with 26% of the voters, near the center of Tennessee
>> - Knoxville <http://en.wikipedia.org/wiki/Knoxville> on Wikipedia,
>> with 17% of the voters
>> - Chattanooga <http://en.wikipedia.org/wiki/Chattanooga> on
>> Wikipedia, with 15% of the voters
>>
>> The preferences of the voters would be divided like this:
>> 42% of voters
>> (close to Memphis)26% of voters
>> (close to Nashville)15% of voters
>> (close to Chattanooga)17% of voters
>> (close to Knoxville)
>>
>> 1. *Memphis*
>> 2. Nashville
>> 3. Chattanooga
>> 4. Knoxville
>>
>>
>> 1. *Nashville*
>> 2. Chattanooga
>> 3. Knoxville
>> 4. Memphis
>>
>>
>> 1. *Chattanooga*
>> 2. Knoxville
>> 3. Nashville
>> 4. Memphis
>>
>>
>> 1. *Knoxville*
>> 2. Chattanooga
>> 3. Nashville
>> 4. Memphis
>>
>> Assume voters in each city support their own city; assist any city within
>> 100 miles; accept any city between 100 and 200 miles; and reject any city
>> that is over 200 miles away or is the farthest city. (These assumptions can
>> be varied substantially without changing the result, but they seem
>> reasonable to start with.)
>> CitySupportAssistAcceptRejectscore
>> Cutoff
>> (must be) <50 >50
>> Memphis 42 0 0 58 (84)
>> Nashville 26 0 74 0 52
>> Chattanooga 15 17 26 42 47
>> Knoxville 17 15 26 42 49
>>
>> Chattanooga and Knoxville both get under 50 points, but Nashville is
>> above the threshold. Thus Memphis, explicitly rejected by a majority, is
>> eliminated. Nashville wins.
>>
>> If Memphis voters tried to strategize by rejecting Nashville in the above
>> scenario, it would have no effect.
>>
>> If Chattanooga and Knoxville tried to strategize by supporting each
>> other, this has a chance of working, but Memphis could safely defend
>> Nashville by assisting it. Since Memphis is essentially guaranteed to be
>> solidly rejected, the Memphis voters have nothing to lose by defensively
>> assisting Nashville like this. A mere 13% of "assist" from Memphis's 42% —
>> that is, under a quarter of the Memphis population — would give Nashville
>> 65 points, more than double the combined size of Chattanooga and Knoxville,
>> safely defending it.
>> Other scenarios explored[edit
>> <http://wiki.electorama.com/w/index.php?title=Majority_score_voting&action=edit§ion=3>
>> ]
>>
>> In all of the scenarios that follow, plurality voting
>> <http://wiki.electorama.com/wiki/Plurality_voting> would get the wrong
>> answer if voters vote honestly, and Majority Score would get the right
>> answer.
>>
>> Say there are two major and several minor candidates (where "major" and
>> "minor" are defined by true support, not simply by media coverage). Voters
>> should reject one major candidate and any minor candidates who are worse;
>> support their favorite, whether they are major or minor; and accept
>> everyone else. In that case, one of the two majors will be rejected by a
>> majority; the other will win; and all minor candidates will show their true
>> support.
>>
>> Now suppose that there are two overall ideological "sides", and the
>> majority "side" is split into two subfactions, each smaller than the full
>> minority "side". This is called the "chicken dilemma
>> <http://wiki.electorama.com/wiki/Chicken_dilemma>", because many voting
>> systems encourage a "game of chicken" between the two majority subfactions;
>> whichever subfaction cooperates less will win, unless cooperation breaks
>> down entirely and the minority wins. A very closely-balanced chicken
>> dilemma would have 27% for subfaction A, 26% for subfaction B, and 47% for
>> the minority Z; whereas a more typical example might have 31%, 24%, and
>> 45%. In Majority Score, each subfaction should support their candidate,
>> accept the other subfaction's, and reject the minority; while minority
>> voters should support their candidate and reject both subfactions. In this
>> case, the bigger subfaction will win.
>>
>> Note that A, the bigger of the two subfactions, must necessarily be above
>> the 50-point threshold in step 2, so Z will be safely eliminated. In many
>> cases, B, the smaller subfaction, will fall short of 50 points. This helps
>> explain the rationale for putting that threshold at 50 points.
>>
>> This is not to say that majority score solves the chicken dilemma 100%.
>> If subfaction B (the smaller one) is larger than 25% of the total, it is
>> still possible for them to win if they largely reject A while the A voters
>> largely accept B. And if both factions largely reject each other, Z can
>> win. But the key word there is "largely"; unlike the case with approval
>> voting <http://wiki.electorama.com/wiki/Approval_voting> or score voting
>> <http://wiki.electorama.com/wiki/Score_voting>, this strategy will not
>> work if it's done by only a few individual voters, but only if one
>> subfaction uses it significantly more often than the other. Also, the
>> smaller subfaction must be larger than 25%, which is rare. Given that
>> organizing such a coordinated betrayal in secret would be hard; that doing
>> so openly would invite mutually-destructive retaliation; and that even if
>> it could be done secretly and unilaterally, it would risk electing Z if the
>> betraying subfaction did not reach 25%; it seems that majority score voting
>> has a good chance of avoiding this problem.
>>
>> As a final tricky scenario, consider what happens in the above case if
>> the minority Z prefers the smaller subfaction B. That results in a center
>> squeeze <http://wiki.electorama.com/wiki/Center_squeeze> scenario: one
>> where candidate B is a Condorcet winner
>> <http://wiki.electorama.com/wiki/Condorcet_winner> (able to beat either
>> rival in a one-on-one race) but an honest plurality loser (with the
>> smallest faction of direct supporters). This is more common than one might
>> think; candidate B is fighting an ideological battle on two fronts, while
>> candidates A and C are free to triangulate towards the middle without
>> losing supporters, so the fact that B has the smallest direct support may
>> not reflect a lack of quality. Thus, generally speaking, as long as each
>> faction considers their second choice to be more than half as good as their
>> first choice (taking the worst choice as 0), it's pretty clear that the
>> Condorcet-winner candidate B is the one who democratically "should" win
>> this election.
>>
>> In this scenario, there are two ways that B could win. B voters could
>> reject both A and C; or A and/or C voters could assist B. Either of these
>> makes strategic sense for the voters in question, and either or both could
>> lead to a strong equilibrium
>> <http://wiki.electorama.com/wiki/Strong_equilibrium> result.
>>
>> One interesting aspect in the above three scenarios: "assist" is only
>> strategically favored in the case of a center squeeze scenario, when the A
>> and C voters are helping B, whom they see as the the "lesser evil", beat
>> the other extreme. If there isn't a center squeeze, voters need only use
>> "support", "accept", or "reject". In fact, even in center squeeze, voters
>> could get by without "assist", as long as enough A and C voters were
>> willing to support B outright. So eliminating the "assist" option would not
>> substantially change the strategic outcome; but it would reduce the
>> expressive power available to the A and C voters in a center squeeze
>> scenario. Thus majority score sacrifices some possible extra simplicity in
>> return for this increased expressive power.
>>
>> It is very rare to have a voting system which can deal with both chicken
>> dilemma and center squeeze. The two situations are very similar, even when
>> voted honestly, and yet the "correct" outcome is different. And under
>> strategic voting in many voting systems, it is very easy for the two
>> different scenarios to lead to identical ballots. Delegated voting systems
>> such as SODA voting <http://wiki.electorama.com/wiki/SODA_voting> can
>> deal with both; but without that kind of explicit participation in the
>> voting process from the candidates, it is very hard to find a system which
>> deals with both types of scenario better than majority score does.
>> Worst case?[edit
>> <http://wiki.electorama.com/w/index.php?title=Majority_score_voting&action=edit§ion=4>
>> ]
>>
>> Majority score could still get a "wrong" answer in cases of a multi-way
>> Chicken dilemma, such that none of the subfactions reached 25%. This
>> scenario is avoidable if the subfactions compensate by "assisting" each
>> other's candidates, but that cooperation is subject to slippery-slope
>> chicken dynamics.
>>
>> If this highly-specific scenario is the most-plausible worst case, it
>> would seem that majority score is a pretty good system.
>> As the first round of a two-round system ("majority score with runoff")[
>> edit
>> <http://wiki.electorama.com/w/index.php?title=Majority_score_voting&action=edit§ion=5>
>> ]
>>
>> If this system is used as the first round of a two-round runoff, then you
>> want to use it to elect at two finalists in the first round. Thus, run the
>> system twice. The first time, replace "50%" in step 2 with "2/3".
>>
>> Then, to find the second winner, if the first-time winner got 1/3 or more
>> support, first downweight those ballots as if you'd eliminated enough of
>> them to make up 1/3 of the electorate. Otherwise, discard all of the
>> ballots which supported first-time winner. After downweighting or
>> discarding, re-tally the points and run Majority Score again.
>>
>> If all the candidates in the first round got a majority of 0's, then you
>> can still find two finalists as explained above. But the voters have sent a
>> message that none of the candidates are good, so one way to deal with the
>> situation would be to have a rule to allow candidates to transfer their
>> 2-votes to new candidates who were not running in the first round, and if
>> those transfers would have made the new candidates finalists, then add them
>> to the second round along with the two finalists who did best in the first
>> round. In that case, since there would be more than two candidates in the
>> second round, it would be important to use majority score for the second
>> round too.
>>
>> Note: this "proportional two-winner majority score" system for the first
>> round is "matrix-summable", that is, summable with O(n²) information per
>> ballot for n candidates. This contrasts with the base majority score
>> method, which is summable with only O(n) information per ballot, and thus
>> can be counted voting equipment designed for counting plurality elections.
>> Relationship to NOTA[edit
>> <http://wiki.electorama.com/w/index.php?title=Majority_score_voting&action=edit§ion=6>
>> ]
>>
>> As discussed in the above section, if all the candidates in the first
>> round got a majority "reject", then the voters have sent a message that
>> none of the candidates are good, akin to a result of "none of the above
>> <http://wiki.electorama.com/wiki/None_of_the_above>" (NOTA). Majority
>> score still gives a winner, but it might be good to have a rule to limit
>> the chance that such a winner would remain in office for multiple terms.
>> This could either be a hard term limit, so that such a winner could only
>> legally serve one term; or perhaps a softer rule that if they run for the
>> same office again, the information of what percent of voters had rejected
>> them should be next to their name on the ballot.
>>
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