Juho Laatu wrote:
I try to summarize my comments in the
form of some rough definitions.
A "simple" method requires
1) a 'simple' method to convert honest
preferences into optimal votes
A "zero-info" method requires
2) this method may not use info about
other voters, but still be able to
convert honest preferences into optimal
votes
A "non-manipulable" method requires
3) it is in everyone's interests to use
the default method to convert honest
preferences into optimal votes
(I didn't cover the "if everyone else uses this method" case.)
These definitions allow also e.g. Approval
to be categorized as (close to) "simple",
not "zero-info" and "non-manipulable".
One more definition to point out one
weakness of Approval.
A "decidable" method requires
1) a method to convert honest preferences into an unambiguous optimal vote
The point is that the there should be
no lotteries that may lead also to
unoptimal votes but the best vote
should be found in a deterministic way.
Approval fails this criterion since
picking the correct number of approved
candidates is sometimes tricky (when
there are more than two strong
candidates).
Since all ranked methods are vulnerable to strategy, what constitutes an
optimal vote depends on the votes of everybody else. Thus no such method
can be either of the above, and any simple method (by the definition)
must also be non-manipulable, since to discover the optimal vote
otherwise, you'd have to know the votes of potentially everybody else.
The definitions you gave could be used for zero info strategy. For instance:
Simple zero-info: The optimal zero-information strategy is simple to
determine.
Dominant zero-info: If everybody uses zero info strategy, and the method
doesn't output a tie, no single voter could gain by changing his vote to
something else.
And there's also the usual zero-info strategy criterion:
No zero-info strategy: The optimal zero information strategy is a
sincere vote.
"No zero-info strategy" implies "simple zero-info". Dominant zero-info
is vaguely similar to SDSC, though the latter deals with
counterstrategies. Dominant zero-info may also be too strong: consider a
situation where the voters produce a "tie minus one vote" (where a
certain ballot can produce a tie); then, if the final voter prefers a
candidate that would be ranked lower to one that would be ranked higher,
he can construct a vote that leads to the two being tied.
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