[EM] The usable interpretation of Jameson's proposed Strong IIAC

[Jameson Quinn]

2013/1/10 Michael Ossipoff <email9648742 at gmail.com>

> On Wed, Jan 9, 2013 at 6:48 PM, Jameson Quinn <jameson.quinn at gmail.com>
> wrote:
>
> >> I suggest that you'll find that no non-probabilistic and
> >> non-dictatorial method can meet Strong IIAC, as defined above.
>
> > I agree. However, they will break it with different probabilities, given
> a
> > universe of scenarios. For a realistic universe, I suggest MJ will break
> it
> > less often than Approval or Score.
>
> But the critrerion's premise stipulates optimal voting. Voting to
> maximize one's utilitly-expectation. That's extreme voting.


Unproven assertion. One which I believe is based on sound logic but faulty
assumptions, and is therefore false.

I would prefer to use "realistic voting" rather than "optimal voting" for
this criterion. Yes, that has an actual, empirically-falsifiable meaning.
However, I believe that you are wrong for both, and if you could prove that
you were right even for "optimal", I would probably have to rethink my
beliefs for "realistic" as well, if not necessarily change them.

...We certainly don't have 0-info elections, as I said earlier.
> In fact, we have non-0-info u/a elections,


Unproven assertion. I believe that for over half the electorate, the
information limits are more salient than the U/A aspects. (Note that
earlier I said that absolute rating was the optimal strategy in the 0-info
limit, *and* that it continued to be an optimal strategy with limited
information for twice as long as for score or probabilistic approval. I
believe that for the majority of voters in the majority of real elections
it will still be optimal.)

Suppose that some set of voters prefer X to Y, and Y to Z. But their
> utility difference for X vs Y is very, very small in comparison to
> their utility difference for X & Y vs Z. Their optimal strategy in MJ
> is to top-rate X and Y, and bottom rate Z.


That depends on their expectations for the medians of X, Y, and Z. In
particular, if they expect at least two of those medians to be below the
second-to-top grade, and the strength of that expectation is greater than
the ratio of the expected instrumental utility of voting to the utility of
an expressive vote (which is almost certain, because the instrumental
utility of voting is infinitesimal), then they will optimally vote Y at
second-to-top. You can even build a quantal-response-type model in which
this is instrumentally optimal.


> Now Z withdraws. Now there
> are only two candidates. Those voters' optmal strategy is now to
> top-rate X and bottom rate Y. If that set of voters is large enough,
> that could change the winner from Y to X.
>

That example works at least as well for Approval or Score; in fact, better,
because neither objection above (expressivity or quantal-response) applies
to either of those.


>
> Why would MJ fail Strong IIAC less often than would Approval and Score?
>
> In particular, in our non-0-info u/a elections?
>

I don't accept this assumption. Obviously I realize that elections are
non-0-info, but I believe they are in practice closer to 0-info than they
are to u/a for most voters in most elections.

Jameson

>
>
>
> > 2013/1/9 Michael Ossipoff <email9648742 at gmail.com>
> >>
> >> Strong IIAC:
> >> -----------------
> >>
> >> Premise:
> >>
> >> An election is held. Everyone votes so as to maximize their utility
> >> expectation, based on their utility-valuations of the candidates, and
> >> their estimates or perceptions of any relevant probabilities regarding
> >> how people will vote, or of count-occurrences such as particular
> >> pair-ties.
> >>
> >> After the election is counted, and the winner recorded, but before any
> >> results are announced to anyone other than the counters, one of the
> >> candidates, who isn't the winner, is hit and killed by a car. Because
> >> a different candidate-set could cause people to vote differently, a
> >> new election is held.
> >>
> >> Again, people vote so as to maximize their expectation, as described
> >> in the first paragraph.
> >>
> >> Requirement;
> >>
> >> The winner of the 2nd election must be the same as the winner of the
> >> 1st election.
> >>
> >> [end of Strong IIAC definition]
> >>
> >> ----------------------------------------------------------------------
> >>
> >> If it sounds as if it would be difficult to determine whether a method
> >> meets that criterion, then I remind you that the example-writer is
> >> free to devise _any_ example that complies with the criterion's
> >> premise. The example-writer can choose a simple but extreme example
> >> with particularly extreme or simplified utilities and probability
> >> perceptions.
> >>
> >
>
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