[EM] [CES #15135] Renaming SARA to "majority score"

[Andy Jennings]

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?

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&section=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&section=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&section=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&section=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&section=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&section=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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