[EM] Fwd: Fwd: Ranked Pairs
Michael Ossipoff
email9648742 at gmail.com
Mon Oct 2 11:32:30 PDT 2023
---------- Forwarded message ---------
From: Michael Ossipoff <email9648742 at gmail.com>
Date: Mon, Oct 2, 2023 at 11:32
Subject: Re: [EM] Fwd: Ranked Pairs
To: Colin Champion <colin.champion at routemaster.app>
You aren’t being very clear with us regarding the sense in which you mean
that margins beats wv at “constant” burial.
With wv, if your candidate is CW, & you refuse to rank candidates outside
your approval-set, then an attempt to use burial to change the winner to
someone outside your approval-set will backfire.
On Mon, Oct 2, 2023 at 06:48 Colin Champion <colin.champion at routemaster.app>
wrote:
> And here, as promised, are some results for strategic voting.
>
> * Constant truncation: WV beats margins for sincere voting, and also for
> compromising and false cycles, but margins beats WV by quite a long way
> (2.7%) for burial.
> * Approval truncation: margins beats WV for sincere voting. The two
> methods almost tie under compromising; margins wins by a long way under
> false cycles (5.5%) and under burial.
> * Candidate-specific truncation: WV beats margins for sincere voting; it
> also wins (slightly more convincingly) under compromising; it loses under
> false cycles and burial.
> * Ignorance truncation: this was essentially a tie under sincere voting
> and remains one under compromising; margins wins slightly under false
> cycles and burial.
>
> Approval truncation takes place before a voter's strategic reordering of
> candidates; other forms of truncation take place after it. In each case I
> measure the accuracy of a voting method in the presence of strategic
> voting, not the vulnerability of the method to manipulation.
> CJC
>
> On 28/09/2023 13:00, Colin Champion wrote:
>
> I tried two other forms of truncation. Under "candidate-specific
> truncation" the m candidates have associated truncation levels which are a
> random permutation of the numbers 1...m. A ballot is truncated to the level
> corresponding to its first candidate. I expected this to be a hard case for
> WV, but in fact it does appreciably better than margins.
> random fptp dblv seq conting nauru
> borda sbc2 bucklin sinkhorn mj av coombs
> 12.6630 35.6490 50.7000 44.9140 51.6650 54.5890
> 73.6530 - 66.3850 - - 53.3880 68.9630
> clower knockout spe benham btr-irv baldwin nanson
> minimax minimaxwv minisum rp river schulze asm cupper
> 70.0190 71.5400 71.7760 71.2680 70.9510 71.4700 71.8440
> 72.0970 72.9090 72.1000 71.5630 71.9420 71.3330 72.2980 75.2630
> condorcet+ random fptp dblv conting borda av
> 70.6780 70.6580 70.9080 71.0760 72.2750 70.9920
> llull+ randomr fptpf fptpr dblvf contingr bordaf
> bordar avf avr minimaxf minimaxr
> 71.6220 71.2570 71.9820 71.2600 71.9970 72.2020 72.0080
> 71.3300 72.0120 72.0510 72.0070
> smith+ randomr fptpf fptpr dblvf contingr bordaf
> bordar avf avr minimaxf minimaxr tideman
> 71.3330 70.8970 71.5080 70.9620 71.5820 72.2730 71.6550
> 71.0270 71.6240 72.0990 71.6490 71.1760
>
> The other form I tried was 'ignorance truncation'. Each candidate has a
> prominence - i.e. probability of being recognised by an arbitrary voter -
> drawn (separately for each election) from a Beta(r,s) distribution. Voters
> rank the candidates they recognise in order of proximity, truncating after
> the last candidate they recognise. I used r=2, s=1, giving a recognition
> probability of 2/3. This was essentially a tie between the two minimax
> variants. Borda, which looked good against other forms of truncation, did
> badly this time. Evidently ignorance truncation is more damaging than the
> other sorts.
> random fptp dblv seq conting nauru
> borda sbc2 bucklin sinkhorn mj av coombs
> 12.5510 37.4290 43.1720 36.6340 41.2690 40.7330
> 34.6170 - 41.5260 - - 40.9330 42.4740
> clower knockout spe benham btr-irv baldwin nanson
> minimax minimaxwv minisum rp river schulze asm cupper
> 43.1770 43.8040 44.4050 43.5870 44.0050 44.0480 43.9970
> 43.9990 43.9330 44.0170 43.8610 44.0040 43.7660 43.6000 46.7470
> condorcet+ random fptp dblv conting borda av
> 43.6260 44.0730 44.1880 43.9420 43.2570 43.5720
> llull+ randomr fptpf fptpr dblvf contingr bordaf
> bordar avf avr minimaxf minimaxr
> 43.7980 43.9980 43.4990 44.0330 43.4980 43.3220 43.4960
> 43.6550 43.4950 43.9890 43.4980
> smith+ randomr fptpf fptpr dblvf contingr bordaf
> bordar avf avr minimaxf minimaxr tideman
> 43.7660 44.1030 43.4060 44.1810 43.4080 43.2570 43.4000
> 43.5750 43.4000 44.0000 43.4100 43.5840
> At risk of repetition... correctness of software is not guaranteed.
> CJC
>
> On 27/09/2023 12:45, Colin Champion wrote:
>
> I have some preliminary results for "approval truncation" in which a voter
> truncates at the largest gap between cardinal rankings. Minimax (margins)
> does slightly better than minimax (WV). Voting is sincere; there are 8
> candidates and 10001 voters (a ballot is truncated on average to 4.6
> entries). Full figures follow (which won't be very readable in a
> variable-width font). It's noticeable that the results are worse than for
> fixed truncation, even though the average ballot length is slightly
> greater.
> random fptp dblv seq conting nauru
> borda sbc2 bucklin sinkhorn mj av coombs
> 12.5820 35.9910 - 45.8790 - 53.6880
> 80.5090 - 67.5170 - - 55.7040 69.1810
> clower knockout spe benham btr-irv baldwin nanson
> minimax minimaxwv minisum rp river schulze asm cupper
> 75.1840 75.8440 76.2830 76.0300 75.8900 75.8700 75.9440
> 75.9660 75.9580 75.9680 75.8200 - 75.7640 75.9200 77.3430
> condorcet+ random fptp dblv conting borda av
> 75.4610 75.5690 75.6860 75.8110 76.4530 75.8300
> llull+ randomr fptpf fptpr dblvf contingr bordaf
> bordar avf avr minimaxf minimaxr
> 75.8750 75.8660 76.2610 75.8330 76.2600 76.3780 76.2620
> 75.9250 76.2590 75.9530 76.2620
> smith+ randomr fptpf fptpr dblvf contingr bordaf
> bordar avf avr minimaxf minimaxr tideman
> 75.7640 75.7470 76.2310 75.7630 76.2400 76.4530 76.2530
> 75.8650 76.2420 75.9680 76.2470 76.0700
> I will try a couple of other truncation models and then look at strategic
> voting.
> CJC
>
> On 24/09/2023 13:41, Colin Champion wrote:
>
> Kevin – thanks for this helpful reply. I'm inclined to favour viewing a
> tie as two half-voters with opposed preferences. I admit that this can only
> be a rule of thumb, but I find it quite persuasive. After all, the whole
> point of ranked voting is that voters start out, I assume, with nebulous
> cardinal judgements in their heads, and that turning these judgements into
> rankings puts them onto a common basis (albeit with loss of information)
> which allows them to be meaningfully combined. The WV rule could easily
> undermine the premise of this procedure.
> I believe that asymmetric treatment of ties in the Borda count leads
> quite directly to errors of the sort I described, but I don't know if this
> is widely accepted.
> It's true that Darlington models ties as genuine expressions of
> indifference. In practice ties can mean almost anything; indifference,
> laziness, ignorance... Quite possibly voting methods which work well for
> one sort of tie will work less well for another. The result I produced
> myself is probably genuine, and indicates that WV is more accurate than
> margins for mandatory truncation; but I was wrong to suppose that it could
> be interpreted more generally since it omits the effect which is most
> likely to work against WV.
> As for the positive arguments you put forward, well they might justify
> a rule of thumb but I wouldn't find them compelling. I don't find the
> Condorcet principle persuasive on its own merits (and do not believe it
> generally sound), but I accept it as a working principle because I don't
> know any other way of obtaining simple accurate voting methods under a
> spatial model.
> I will try to extend my own evaluation software to allow a less
> restrictive model of truncation.
> Colin
>
> On 23/09/2023 02:47, Kevin Venzke wrote:
>
> Hi Colin,
>
> Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion <colin.champion at routemaster.app> <colin.champion at routemaster.app> a écrit :
>
> A possible explanation for the discrepancy between my result and Darlington's is that
> in my evaluation every ballot had the same number of ties and in Darlington's the
> numbers differed.
> On the face of it, WV doesn't treat voters equally. If we defined "winning votes" as
> "the number of voters who prefer A to B plus half the number who rank them equally",
> then every voter would contribute m(m-1)/2 winning votes and WV would be equivalent
> (I think) to Margins. But instead we define winning votes asymmetrically so that WV
> is *not* equivalent to margins but voters contribute different numbers of winning
> votes depending on the number of ties in their ballots. I can imagine this leading to
> artefacts which Darlington's evaluation would pick up and mine would miss. If this is
> what happened, then even Darlington's evaluation must be too lenient to WV since he
> doesn't include effects which would in fact arise, such as voters truncating
> differentially according to their political viewpoint.
> Maybe these things have been taken into account; I have no idea, having never seen the
> thinking behind WV.
>
> I am not sure what to make of Darlington's defeat strength comparison. It sounds like
> it was basically a simulation of sincere voters who vote equality because they actually
> consider the candidates equal. That premise is fine but somewhat far removed from how
> this topic is usually discussed, i.e. with some consideration of comparative strategy.
>
> I notice incidentally that Darlington says incorrectly on page 22 that MinMax(PO) is a
> Condorcet method. I wonder whether he implemented it as one to get his numbers on that.
>
> In any case:
>
> To find the motivation for WV I would start with first principles. How should we design
> a Condorcet completion method to minimize strategic incentives? A motivation behind
> Condorcet itself is that voters should not vote sincerely only to find that they
> should've voted another way.
>
> What could this mean here? Well, a full majority can always get what they want by
> changing their votes. Therefore if a majority votes A>B yet B is elected, we have
> *probably* done something wrong, because the majority certainly did have the power to
> make A win instead. The election of B gives the A>B voters an incentive to vote
> differently to change the outcome. The voters obtain a "complaint," I will call it.
> Since majorities will most predictably obtain such complaints when we override their
> preference, we should prioritize locking majorities.
>
> With WV, there is no special heed paid to majorities, it just goes down the list of
> contests starting with the largest winning blocs. But this achieves the goal. It
> applies its principle to sub-majority contests as well, and maybe this is good bad or
> neutral, but maybe we can believe that if it was helpful (for our end goal) to favor
> majorities over sub-majorities then it could also be helpful to favor larger
> sub-majorities over smaller sub-majorities. It certainly stands to reason that the more
> voters you have sharing some stance, the more likely it is that a vote change on their
> part could change the outcome.
>
> (On my website I describe a different approach focused on compromise incentive, and
> measuring the potential for this more directly, and one can take that as me suggesting
> that WV actually leaves some room for improvement.)
>
> You notice that adding half-votes to equal rankings under WV will turn it into margins.
> This would give every contest a full majority on the winning side, and seemingly we can
> trivialize this requirement of mine to prioritize majorities.
>
> But I think it's clear, in the context of this analysis, that adding half-votes for
> equal rankings doesn't make sense. The voter who says A=B doesn't turn into a pair of
> opposing "half-complaints," where one of the complaints has the potential to be voiced
> when *either* of A or B is elected. The A=B voter has no possible complaint either way,
> as neither result can incentivize them to change their vote.
>
> Additionally, I think that voters expect and want it to be the case that abstaining
> from a pairwise contest does not mean the same thing as saying they rate both
> candidates equal. I touched on this in my previous post.
>
> Consider this election:
>
> 7 A>B
> 5 B
> 8 C
>
> Margins elects A, which is very unusual across election methods, and I think most
> people would find this result surprising due to a sense of what truncation ought to
> mean.
>
> (Consider copying it into votingmethods.net/calc to see margins and MMPO stand alone
> here.)
>
> Perhaps with enough education people can *understand* that the method takes seriously
> the apparent equality of the truncated preferences. But I don't think voters will find
> it comfortable to vote under those circumstances. I think voters want to be able to
> identify the set of candidates that they believe they are trying to defeat, leave them
> out of their ranking, and not have to think any further about it.
>
> Kevinvotingmethods.net
>
>
>
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