[EM] Voting Criteria 101, Four Criteria

Benjamin Grant benn at 4efix.com
Mon Jun 17 09:36:21 PDT 2013

```> -----Original Message-----
> From: Kristofer Munsterhjelm [mailto:km_elmet at lavabit.com]
> Sent: Monday, June 17, 2013 12:09 PM
> Subject: Re: [EM] Voting Criteria 101, Four Criteria
>
> On 06/16/2013 06:55 PM, Benjamin Grant wrote:
> > *Name*: *_Plurality_*
> >
> > *Description*: If A gets more "first preference" ballots than B, A
> > must not lose to B.
>
> Be careful not to mistake Plurality, the criterion, from Plurality the
method.
> Plurality, the criterion, says: "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".
>
> The Plurality criterion is only relevant when the voters may truncate
their
> ballots. In it, there's an assumption that listed candidates are ranked
higher
> than non-listed ones - a sort of Approval assumption, if you will.
>
> To show a concrete example: say a voter votes A first, B second, and
leaves C
> off the ballot. Furthermore say nobody actually ranks C. Then C shouldn't
> win, because A has more first-place votes than C has any-place votes.

OK, that makes sense.

> > *Name: _Majority_*
> > *Thoughts*: I might be missing something here, but this seems like a
> > no-brainer. If over 50% of the voters want someone, they should get
> > him, any other approach would seem to create minority rule? I guess a
> > challenge to this criteria might be the following: using Range Voting,
> > A gets a 90 range vote from 60 out of 100 voters, while B gets an 80
> > from
> > 80 out of 100 voters. A's net is 5400, but B's net is 6400, so B would
> > win (everyone else got less).  Does this fail the Majority Criterion,
> > because A got a higher vote from over half, or does it fulfill
> > Majority because B's net was greater than A's net??
>
> There are usually two arguments against the Majority criterion from those
> that like cardinal methods.
>
> First, there's the "pizza example": say three people are deciding on what
piza
> to get. Two of them prefer pepperoni to everything else, but the last
person
> absolutely can't have pepperoni. Then, the argument goes, it would be
> unreasonable and unflexible to pick the pepperoni pizza just because a
> majority wanted it.
>
> Second, there's the redistribution argument. Consider a public election
> where a candidate wants to confiscate everything a certain minority owns
> and then distribute the loot to the majority. If the electorate is simple
> enough, a majority might vote for that candidate, but the choice would not
> be a good one.
>
> Briefly: the argument against Majority is "tyranny of majority". But
ranked
> methods can't know whether any given election is a tyranny-of-majority
one,
> and between erring in favor of the majority and in favor of a minority
(which
> might not be a good minority at all), the former's better. Condorcet's
jury
> theorem is one way of formalizing that.

In my (limited) experience, every instance where there has been an
allegation of tyranny of the majority, the reverse choice is something even
worse, tyranny of the minority. While ultimately certain things, like human
rights, shouldn't be a matter for voting at all, if something deserves a
vote it probably deserves to serve the greatest good for the greatest
number.

To take your pizza analogy, if the two people *only* want pepperoni, it
would be selfish of the third to expect the majority to bend to his desires.
On the other hand, if the two people are already fine with *either*
pepperoni or plain, then they will say so.

Ultimately, the only time I find when people complain about the tyranny of
the majority is when they are in a minority that doesn't want what the
majority truly does - and that's just the downside of not being a dictator.

So I guess I would say this - whenever you hear the phrase tyranny of the
majority, you can probably indentify the speaker is *usually* someone who
wants more power over the selection process than they ought to have.

> > *Name: _Participation_*
> >
> > *Description*: If a ballot is added which prefers A to B, the addition
> > of the ballot must not change the winner from A to B
> >
> > *Thoughts*:  This seems to make sense. If we do not require this, then
> > we permit voting systems where trying to vote sincerely harms your
> > interests. Also, any voting system that would fail Participation would
> > be I think fragile and react in not always predictable ways - like IRV.
> > SO this seems to me to be a solid requirement, that I can't imagine a
> > system that failed this Criterion to have some other benefit so
> > wonderful to make failing Participation worth overlooking - I cannot
> > imagine it.
>
> Welcome to the unintuitive world of voting methods :-) Arrow's theorem
> says you can't have unanimity (if everybody agrees that A>B, B does not
> win), IIA (as you mention below) and non-dictatorship. Since one can't
give
> up the latter two and have anything like a good ranked voting method, that
> means every method must fail IIA.

Wow.  I am just starting to get exposed to this stuff, but it is being a
bitter pill to swallow that it is mathematically impossible to have one
voting system fulfill several desirable criteria - that these criteria might
be incompatible.  Ultimately, I guess I will have to figure out which
criteria are incompatible with which, and determine among my choices which I
need and which I don't.  Taking notes here.

> There's also a heuristic argument that IIA is too strong. It goes that the
> introduction of additional candidates may tell you that things aren't the
same
> before and after the introduction of the same candidates. See
>
https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Critic
ism_of_IIA
>
> Also note that IIA and majority is incompatible. The same link shows why.

I "deconstructed" Majority in another post, I wonder if this address IIA
compatibility with what I was left with?

Thanks for your thoughts, they help! :)

-Benn Grant
eFix Computer Consulting
benn at 4efix.com
603.283.6601

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