[EM] Question about the Plurality Criterion

Benjamin Grant panjakrejn at gmail.com
Mon Jun 24 14:30:55 PDT 2013

```On Mon, Jun 24, 2013 at 4:45 PM, Kristofer Munsterhjelm <
km_elmet at lavabit.com> wrote:

> On 06/24/2013 04:10 PM, Benjamin Grant wrote:
>
>> As I have had it explained to me, the Plurality Criterion is: "If there
>> are two candidates X and Y so that X has more first place votes than Y
>> has any place votes, then Y shouldn't win".
>>
>> Which I think means that if X has, for example, 100 votes, then B would
>> have to appear on less than 100 ballots and still **win** for this
>> criterion to be failed, yes?
>>
>> I cannot imagine a (halfway desirable) voting system that would fail the
>> Plurality Criterion – can anyone tell me the simplest one that would?
>> Apart from a lame one like “least votes win”, I mean?
>>
>
> That depends on what you put into a candidate not being ranked on the
> ballot. If you think that voters mean that all the candidates they rank are
> better than those they don't rank, then Plurality obviously makes sense. On
> the other hand, if not ranking a candidate simply means the voter has no
> opinion, then the Plurality criterion is no longer as obvious.
>

Yeah, I am starting to get that - that is a critical choice to make in
crafting and executing the system.

> A very simple system that fails the Plurality criterion for this reason is
> mean (average) Range. In this system, you take the mean rating of each
> candidate, and greatest mean wins; but in this particular variant, if you
> don't rate candidate X, you don't change his mean in any way.
>
> So you could have a candidate A that's ranked with a mean of 8.5 by 1
> million voters, and a candidate B that's ranked with a mean of 9 by 500 000
> voters (and otherwise not ranked). Say more than 500k of the ballots list A
> first. Then B is barred from winning by the Plurality criterion. Yet by the
> logic of mean Range, B should win because, according to that logic, the
> voters who didn't list B were just saying they didn't *know* what rating B
> should have and instead left the task of determining B's mean to the others
> who did rate B.
>
> Now, pure mean Range has a problem in that candidates who are only known
> by a few fanatics could get an illegitimate win, so some sort of soft
> quorum (like IMDB does for its movies) is probably better. I just use mean
> Range as an example of a system that isn't obviously insane yet fails the
> Plurality criterion (or one particular way the Plurality criterion might be
> extended to rated ballots).
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>

Interesting - to wrap my brain around this going to have to create some
exmaple fake elections with these stats, will reply back once I have, could
be a day or more.

-Benn
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