Woodall free riding uses some irrelevant candidate that is ranked first.
Hylland free riding does not rank the favourite candidate.
A third approach to free riding is to rearrange the candidates to
reflect the estimated probabilities.
The true preference order of a voter is A>B>C>D>E>... The voter
expects A to be elected quite certainly. Candidates B and C are less
certain. The voter considers B and C to be almost as good as A.
Candidates starting from D are considerably worse. As a result the
voter decides to vote B>C>A>D>E>...
This strategy increases the probability of B or C to be elected. If B
and C are not elected the vote goes to A (not lost in the case that A
needs more votes since it gets less votes than expected (due to
strategic voting or for other reasons)). It is possible that B or C
gets elected while A will not, but the risks are not too big. In any
case the three clearly best candidates (A, B, C) will get all
possible power of this vote. There is also no risk of the vote going
to some irrelevant candidate (as in Woodall free riding).
This generalizes to any preference order, not only to the handling of
the first favourite. The voter can estimate the probabilities of all
candidates to become elected (also taking into account the impact of
strategic voting) and the rearrange the whole preference list based
on the estimated probabilities and the personal utility of each
candidate.
The resulting strategic preference order could resemble that of
Woodall free riding if there is a candidate that very certainly will
not be elected. The utility of that candidate may be quite low.
The resulting strategic preference order could resemble that of
Hylland free riding if the probability of the favourite candidate is
very high. That candidate would however be listed somewhere close to
the end of the list.
Juho
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