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

[Michael Ossipoff]

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. That's
voting as in Approval. Score's optimal strategy is known too: extreme
voting.

Optimal voing is a fair stipulation for a Strong IIAC.

You said that MJ's 0-info optimal strategy is utility-proportional
rating. We certainly don't have 0-info elections, as I said earlier.
In fact, we have non-0-info u/a elections, in which the optimal
strategies of MJ, Approval and Score are to top-rate the acceptables
and bottom rate the unacceptables.

> I realize that the above claim is unsubstantiated. But note that I above
> agree with an unsubstantiated claim.

For this purpose, it isn't necessary to prove that all
non-probabilistic, non-dictatorial methods fail Strong IIAC. It's
enough to say (and demonstrate it if necessary) that MJ fails it.

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. 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.

Why would MJ fail Strong IIAC less often than would Approval and Score?

In particular, in our non-0-info u/a elections?



> 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.
>>
>