[EM] Fwd: Ranked Pairs

[Colin Champion]

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>  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.
>>
>> Kevin
>> votingmethods.net
>
>
> ----
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