[EM] A method "DNA" generator, tester, and fixer

[Juho]

On May 27, 2010, at 4:07 AM, Kevin Venzke wrote:

> Hi Juho,
>
> --- En date de : Mer 26.5.10, Juho <juho4880 at yahoo.co.uk> a écrit :
>>>>>> The following criterion is similar to
>>>> Plurality.  Does
>>>>>> it have a name?
>>>>>>
>>>>>> If the number of ballots on which X beats
>> Y is
>>>> greater than
>>>>>> the number of
>>>>>> ballots on which Y is ranked, then Y
>> cannot be
>>>> elected.
>>>>
>>>>>> Any decent method that doesn't satisfy
>> it?
>>>>>
>>>>> This criterion is strictly stronger than
>> Plurality, so
>>>> I'd have to ask
>>>>> whether you think any decent methods fail
>> Plurality.
>>>> Probably the answer
>>>>> is no, not really.
>>>>
>>>> This says that all typical margins based Condorcet
>> methods
>>>> would not be "decent". One could ask the question
>> also in
>>>> the reverse direction. All methods violate some
>> criteria
>>>> that look good at least at first sight. Which
>> property of
>>>> the plurality criterion (or the new criterion)
>> makes it a
>>>> mandatory requirement for all election methods (or
>> Condorcet
>>>> or ranked methods)?
>>>
>>> Personally I would allow Plurality failures for a good
>> reason.
>>>
>>> But I think that most people would generally not be
>> accepting. This would
>>> be because of a view that there is such a thing as
>> "support" involved in
>>> voting for a candidate and this can't be found when
>> one truncates a
>>> candidate. So when you compare a candidate X who is
>> the favorite of 10
>>> voters, and you can't find that many voters who
>> "support" Y on their
>>> ballots in any way, something seems wrong when Y wins.
>> The thought is
>>> why would you ever need to elect Y when you could just
>> elect X? It's
>>> similar to Pareto in that sense.
>>
>> Yes, in ballots where the position of truncated (or shared
>> last) candidates looks clearly different than the position
>> of other candidates the voters may get the impression that
>> thy are supporting all others and not supporting the
>> truncated / shared last candidates. And they may vote this
>> way and dislike methods that do do not respect their
>> impression on what should happen with respect to candidates
>> with lots of first preferences vs. candidates with less any
>> higher than last preferences. But on the other hand all
>> methods need not have such implicit approval/support
>> assumptions.
>
> Well, you can argue with voters or you can argue with me. I personally
> don't see value in what margins wants to substitute, so I don't see
> that margins has a good reason for failing Plurality.

The reason could be related to the margins concept (level of  
opposition against the winner as measured in margins) or strategies.  
For example with votes 48: A>B, 3: B, 49: C margins (typically) elects  
A but plurality criterion says that in deterministic methods the  
winner must not be A. If B would win (as in typical WV methods) then  
there would be complaints "why did B win although A beats B with a  
huge margin". If C would win (as in IRV) then the complaints would  
maybe be milder, but A's worst defeat in margins is anyway smaller  
than C's although C has 1% worth more first preferences than A. On the  
strategy side the sincere opinion of the B voters was maybe B>A. In  
that case the 3% strategic voters stole the victory quite easily from A.

>
>> It depends also a lot on the environment if one should
>> optimize the method so that it will perform well under all
>> (sincere and/or strategic) circumstances or if it should
>> look good to the average voters and politicians so that it
>> will have a chance of getting adopted. If one wants e.g. to
>> promote Condorcet methods one could (in theory) listen to
>> the discussion for a while and then pick a method that looks
>> best in the observed discussion environment (the behaviour
>> of all Condoret methods is anyway quite similar in typical
>> elections).
>
> They are similar but whether the different incentives are significant
> can't easily be proven.

Yes. In this example we are probably talking more about efficient  
campaign, propaganda and claims towards media, politicians and regular  
voters than about mathematical proofs.

>
>> There could be also other criteria that people want to see
>> implemented. They might for example hate "favourite
>> betrayal", and that could make all Condorcet methods
>> unusable. If people study election methods in detail they
>> must accept that all the best election methods will violate
>> some nice looking criteria.
>
> Yes. If I thought that Forest thought failing FBC was unacceptable  
> then
> when I guess whether an FBC-failing method is decent to him, I would
> say probably not. If he thinks Mono-add-top is crucial and Plurality  
> is
> not then I guess margins is a decent method for him.

Yes, all good good looking criteria. One more key criterion that was  
not mentioned yet is later-no-harm.

>
>> Btw, in the example above I guess the plurality criterion
>> doesn't requite that X should win. Also some other candidate
>> with sufficient number of above last rankings could win. In
>> that sense methods that meet the plurality criterion might
>> not be an exact match to the needs of that voter who wanted
>> X to win with 10 votes.
>
> There is no voter who wanted X to win. The issue is that it is cut and
> dry that X is better than Y; Z may be better than either but we may  
> not
> be able to easily show it. It's no different from Pareto there.

Yes, typically we are talking about cycles where there is always an  
argument why someone else is better than the winner. (When there are  
cycles many voters might actually consider some random tie solving  
method to be a fair method.)

Juho


>
> Kevin
>
>
>
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