# [EM] IRV and Brown vs. Smallwood

peter barath peb at freemail.hu
Sun Apr 5 07:48:47 PDT 2009

```> Yet me give you an example
> Vote for mayor:
> We have three candidate running for mayor
> Vote for one:
> [  ] Smith
> [  ] Jones
> [  ] Johnson
>
> If Smith has the least number of votes and is eliminated then who
> would you vote for.
> [  ] Jones
> [  ] Johnson
>
> If Jones has the least number of votes and is eliminated then who
> would you vote for.
> [  ] Smith
> [  ] Johnson
>
> If Johnson has the least number of votes and is eliminated then who
> would you vote for.
> [  ] Smith
> [  ] Jones
>
> This is clearly consistent with one-person one-vote.
> Every voter votes once and all voters are treated equal.
> You could say that each voter is voting twice once in the first part
> and a contingency vote in the second part depending on who is
> eliminated. This is conceptually the same as IRV method, with one
> exception. IRV assumes voters are rational and that the votes are
> independent.
> In this example a voter could vote for Jones on the first part and
> if Smith is eliminated then vote for Johnson in the second part.
> It is hard to understand the rationality of this kind of vote.

For punctuality's sake: I think this kind of vote would be rare,
but sometimes rational.

400: Smith, Jones, Johnson
300: Jones, Smith, Johnson
600: Johnson, Jones, Smith

and I happen to belong to the latest, estimatedly 600 strong group.

I am afraid to vote first for my favourite Johnson, because
Jones is likely to drop first, and then the hated Smith is
almost sure to win.

So I make a compromise and vote for Jones, sacrificing my
favourite Johnson.

Suppose that my estimation proves to be wrong - it can happen
even to a rational person - and Smith drops first. Then I would
happily vote for Johnson.

The thing can happen even without wrong estimation. If we
Johnsonists are smart enough then 150 of us vote for Jones and
450 vote for Johnson, so we _make_ Smith drop first.

Of course, we don't have much hope to win in the second round
but no reason for not to try.

Still I don't think IRV violates the one person one vote
principle. This principle is not to apply in a what-would-
happen-if-using-not-this-but-another-method style. The
question is what a vote is. If a vote is a paper which
can be filled, then of course IRV is one person one vote.
If a vote is a checkmark on a paper then of course IRV
is one person one vote. The principle doesn't say a person
have one vote in her entire life! Of course, a paper can
contain one first vote, one second vote, one third vote
and so on, as long as these possibilities are for everyone.
The voter has the right not to use all thiese votes - in the
US, voting is not compulsory (yes, I know there are countries
where it is).

Peter Barath

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