Jobst Heitzig wrote:
Dear Warren,
I don't seem to understand the definition:
A single-winner voting system "fails the NESD property" if, when every
honest voter
changes their vote to rank A top and B bottom (or B top and A bottom;
depends on the voter which way she goes), leaving it otherwise
unaltered, that always (except in very rare "exact tie" situations)
causes A or B to win.
So, when all voters vote strategic (i.e. no voter is honest) and all
leave their ballots unchanged, then by definition "every honest voter
changes their vote to rank A top and B bottom" but of course no system
changes the result since no ballot is changed. Hence no system fails NESD.
What is the misunderstanding here?
I think he means:
Call the first group of ballots, X, consisting of ranked ballots made by
honest voters. Now take every ballot in X and, for each ballot y, if y
votes A > B, put A first and B last, or if y votes B > A, put B first
and A last, leavin the ballot otherwise unchanged. Call the modified
bundle, consisting of these modified y-ballots, X'.
If there exists such a group of ballots X so that the method in question
gives a different victor when fed X and when fed X', and gives either A
or B as the victor for group X', then it fails the NESD property.
In other words: if the entire electorate decides that the dangerous
contest is A vs B and so maximally buries the one they like the least,
and this strategy pays off, then it fails this property.
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