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Dear Marcus,<br>
<br>
You wrote (Tues.Jun.15):<br>
<br>
"This is Steve Eppley's "Non-Drastic Defense" criterion:<br>
<pre>><i> Non-Drastic Defense: Each voter must be allowed to vote
</i>><i> as many alternatives tied for top as she wishes, and for
</i>><i> all x e A, x must not be elected if there exists y e A
</i>><i> such that that more than half of the voters vote y over x
</i>><i> and no worse than tied for top.
</i>
Here is an example where ER-IRV(fractional) violates
Steve Eppley's "Non-Drastic Defense" criterion:
20 A=B=C>E>...
20 A=B=D>E>...
20 A=C=D>E>...
7 B>E>...
7 C>E>...
7 D>E>...
38 E>...
A majority of the voters strictly prefers candidate A
to candidate E and ranks candidate A tied for top.
Nevertheless, candidate E is the winner."
CB: Thanks for your interest and good example. Maybe somwhat confusingly, Steve Eppley gives two
versions of this criterion (same name and author, but slightly different definitions).
Here is the other one:
</pre>
<blockquote type="cite"><i> non-drastic defense</i>: If more than half of
the voters prefer alternative <i>y</i> <br>
over alternative <i>x</i>, then that majority must have some way
of voting <br>
that ensures <i>x</i> will not be elected and does not require any
of them <br>
to rank <i>y</i> over any more-preferred alternatives. (This is
promoted by <br>
Mike Ossipoff under the name <i>Weak Defensive Strategy Criterion</i>. <br>
Non-satisfaction means some members of the majority may need to <br>
misrepresent their preferences by voting a compromise alternative <br>
over favored alternatives if they want to ensure the defeat of less-<br>
preferred alternatives.) </blockquote>
CB: In your example, y is A and x is E. The top three groups of voters,
who all ranked A equal first with two other candidates, can<br>
ensure that E is not elected by ranking A alone in first place. There is
no candidate that they prefer to A, so ER-IRV(fractional) seems<br>
to meet this version (as Mike Ossipoff in effect claimed).<br>
<br>
Chris Benham<br>
<br>
<br>
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