[EM] Fwd: Fwd: Ranked Pairs
Colin Champion
colin.champion at routemaster.app
Tue Oct 3 02:01:49 PDT 2023
Michael – apologies. By the 'sincere winner' I mean the candidate who
would win in the absence of strategic voting. By 'constant truncation' I
mean all voters truncating to the same number of candidates. This models
the mandatory truncation which is imposed in some elections, in which a
voter is limited to ranking (eg.) 3 candidates. It differs from
truncation to differing numbers of candidates such as would arise from
voter indifference or incomplete knowledge.
If Condorcet methods are intended to elect the Condorcet winner,
then I suppose they're 100% successful. For that matter the Borda count
is 100% successful at electing the Borda winner.
You wrote "if your candidate is CW... then an attempt to use burial
to change the winner to someone outside your approval-set will backfire"
which I understood as implying that "you" were the burier. Perhaps you
meant that if Ursula, a supporter of B, refuses to rank anyone outside
her "approval set", then if another voter Veronica tries to change the
winner from B to A (who is not in Ursula's approval set) then the
attempt would backfire.
Colin
On 03/10/2023 09:13, Michael Ossipoff wrote:
>
> Colin—
>
> The incomprehension is indeed reciprocal. In this message I’ll try to
> reduce it, if not resolve it.
>
> These matters have been very much & very thoroughly discussed here, a
> long time ago. It might be best to either accept the consensus here,
> or to unassertively ask questions, to find out what the terms mean &
> why we say what we say.
>
> Don’t invent theory & tell us how it is.
>
> You have basically the right idea of what truncation & burying are.
>
> What you call “the rightful winner” is the social-utility maximizer.
> The Condorcet methods are intended to elect the Condorcet winner.
>
> You mention a 3rd winner you call the “sincere winner”. …presumably
> different from the Condorcet winner & the rightful winner. You didn’t
> say what you mean by that term.
>
> You’ve again spoken of “constant truncation”. How is that different
> from ordinary truncation? One habitually does it in every election?
>
> Did I say that the burier is trying to elect someone outside his own
> approval set?
>
> …or that the buriers’ candidate is the CW?
>
> Please try to be sure what you’re replying to, & what you mean, before
> posting.
>
> That “exonerated” post was about properties of the winning-votes
> methods. …properties that we discussed & agreed about long ago.
>
> Offensive truncation won’t work
>
> Offensive burial backfires if the CW’s voters haven’t ranked the
> buriers’ candidate.
>
> So, if you (a preferrer of the CW) refuse to rank anyone not in your
> approval set, then burial intended to change the winner from the CW to
> someone outside your approval set will backfire, & is thereby deterred.
>
> Michael Ossipoff
>
> On Tue, Oct 3, 2023 at 00:11 Colin Champion
> <colin.champion at routemaster.app
> <mailto:colin.champion at routemaster.app>> wrote:
>
> Michael - the incomprehension is reciprocal. By burial I mean that
> the supporters of one candidate A insincerely relegate another
> candidate B to the bottom of their ballots. This is considered to
> be successful if it leads to a candidate C winning who is closer
> to A than the sincere winner is (where C may or may not be equal
> to A). I assume that strategic voting will be attempted only when
> it will succeed since I make no attempt to model imperfect knowledge.
> The rightful winner is the candidate whose average distance
> from voters is least. A voting method is deemed correct in an
> election if it elects the rightful winner in spite of any attempt
> at burial (i.e. against every (A,B) combination).
> With constant truncation, the relegated candidate is simply
> truncated off. So, truncating from 8 to 4, if A's supporters agree
> to bury B, and if B occurs in the top 4 positions of a voter's
> ranking, then B is moved to the voter's discards and the ballot is
> reduced to 3 candidates. If B is outside the top 4 positions, then
> the burial has no effect.
> The likeliest case of successful burial is the opposite of the
> case you say cannot happen. It arises when B is simultaneously the
> Condorcet winner, the sincere winner and the rightful winner, and
> when A obtains victory as a result of his supporters burying B. In
> this case the buriers are *not* trying to change the winner to
> someone outside their approval set and their candidate is *not*
> the CW. I wonder whether your wording corresponds to your
> intentions, or whether I simply misunderstand it.
> I'm afraid I also don't really understand your 'exonerated'
> post, but it probably isn't directed at me.
> Colin
>
> On 02/10/2023 19:32, Michael Ossipoff wrote:
>>
>>
>> ---------- Forwarded message ---------
>> From: *Michael Ossipoff* <email9648742 at gmail.com
>> <mailto: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
>> <mailto: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
>> <mailto: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> <mailto: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 intovotingmethods.net/calc <http://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.
>>>>>>
>>>>>> Kevin
>>>>>> votingmethods.net <http://votingmethods.net>
>>>>>
>>>>>
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