[EM] Fwd: Fwd: Ranked Pairs
Colin Champion
colin.champion at routemaster.app
Tue Oct 3 00:10:48 PDT 2023
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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