[EM] Single Contest

[Jameson Quinn]

The ranked majority criterion is: if one candidate is top-ranked by a
majority of voters, that candidate must win.

To me, the natural extension of that to rated systems is: if only one
candidate is top-rated by any majority of voters, that candidate must win.

You are suggesting that we use the ranked majority criterion for rated
systems. If we do so, you are right that broad classes of rated systems
(including range, median, and chiastic) can never pass.

But if we use my definition of the criterion, then median systems pass,
trivially.

JQ

2011/7/24 Andy Jennings <elections at jenningsstory.com>

> On Sat, Jul 23, 2011 at 11:28 AM, <fsimmons at pcc.edu> wrote:
>
>> If one of the finalists is chosen by a method that satisfies the majority
>> criterion, then you can skip step
>> one, and the method becomes smoother.
>>
>> Here are some possibilities for the method that satisfies the majority
>> criterion:  DSC, Bucklin, and the
>> following range ballot based method:
>>
>> Elect the candidate X with the greatest value of p such that more than p/2
>> percent of the ballots rate X at
>> least p percent of the maxRange value.
>>
>
> Forest,
>
> Can you clarify your definition of the majority criterion?  I don't think
> this method satisfies it.
>
> As a general example, suppose there are two candidates, A and B.  The
> voting range is 0-100 and there are 5 voters:
> 1 voter: A=10 B=30
> 1 voter: A=30 B=50
> 1 voter: A=50 B=70
> 1 voter: A=70 B=90
> 1 voter: A=90 B=10
>
> B is strictly preferred to A by 4 out of 5 voters, but these two candidates
> have the exact same set of votes.  Any method which forgets which voter gave
> which vote must consider them exactly tied.  This includes score (range)
> voting, majority judgement, the chiastic median, and any of the other
> generalized medians.  Thus, with only some minor perturbation, A can defeat
> B in any of these methods.
>
> In the chiastic median (or the majority judgement), both candidates have
> societal grades of 50, but if you change A=50 to A=51 for the third voter,
> A's societal grade becomes 51 and A defeats B, despite strong majority
> opposition.
>
> In the p/2 system, 40% of the voters gave grades of 70 or above and 20% of
> the voters gave grades strictly above 70, so both candidates get a societal
> grade of 70.  But if you change A=70 to A=71 for the fourth voter, A's
> societal grade becomes 71 and A defeats B, again despite a strong majority
> opposition.
>
> I think any method which forgets which voter gave which vote will never
> satisfy the majority criterion.
>
> - Andy
>
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