[EM] Approval and ICC

[MIKE OSSIPOFF]

>Approval has no such problem because the Bush supporters can simply vote 
>for both Bush-A and Bush-B. If they tie, a coin is flipped and one is 
>elected. Since they are exact clones, either one will do.

Clones aren't necessarily identical. People who prefer the clone set to all 
others can have significant preferences among the clones, as can all the 
other voters.

That's why Approval meets IICC, but not ICC.

ICC is more demanding, requiring that changing the size of a clone-set not 
change the matter of whiether the winner comes from that set, as long as 
everyone votes sincerely.

Because the candidates in a clone set are not identical, and the supporters 
of the clone set may have significant preferences among them, Approval can 
get into trouble with a clone set.

Say you like Kucinich, and vote for him only in Approval, and he wins. Then 
Nader is added to the election, and there's another vote. Say Nader & 
Kucinich are clones. Regardless of that you may like Nader so much more than 
Kucinich that you want to vote Nader over Kucinich.

Just because Nader and Kucinich are clones doesn't mean that your preference 
between them isn't strong enough, compared to your preference for Kucinich 
over the others, to give you good reason to vote only for Nader. I emphasize 
that, depending on your probability estimates, it isn't necessarily bad 
strategy to vote only for Nader under those conditions.

With Approval, that clone set can lose even though you vote sincerely. With 
Approval, sincere voting doesn't guarantee that a clone set's win won't be 
affected by changing its number of candidates.

That's why Approval fails ICC, though it meets IICC.

With BeatpathWinner, sincerely voting Nader over Kucinich won't change the 
fact that BeatpathWinner protects the clone set from losing a win because of 
a new clone.

Mike Ossipoff

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