[EM] LNH, Mono-Add-Top, etc
nkklrp at hotmail.com
Sun Dec 28 21:54:02 PST 2003
"Mono-add-top" is a Woodall criterion which says that adding ballots that
first-preference to X must not harm X. It is met by IRV and Margins, but not
I'm not necessarily denying that, but can you demonstrate that those
statements are correct?
Aside from that question, there are very many criteria, and all are failed
by some methods.
It's been shown that all nonprobabilisitic methods can have incentive for
Predictably, different methods often have different strategy. Of those
innumerable criteria, different methods meet different criteria.
Any criterion can be justified by someone saying "This criterion is
important". In that way, there are a vast number of important critreria. A
vast number of essential criteria, and no method meets them all.
When any one type of strategy incentive is looked at, it always looks
undesirable, and a good-sounding argument can be made against whatever
method has that strategy incentive. That's why you should keep in mind that
no nonprobabilistic method is strategy-free. So it's a question of what kind
of strategy incentive is worse.
No one can establish that one standad is more important than another. So,
when asserting the importance of one's favorite standard, one is always
safe from being contradicted.
Majority rule is a widely accepted standard. The lesser-of-2-evils problem
is notorious. With only very few exceptions, nearly all single-winner reform
advocates want to get rid of that problem. The goal of getting rid of the
lesser-of-2-evils (LO2E) problem therefore is a widely held standard, as is
It's been shown here that wv and, in some ways, Approval too, beats Margins
and IRV by those 2 very widely-recognized standards.
Say a majority of the voters prefer X to Y. Y is a "greater-evil" whom they
don't want to win. What must they do in order to keep Y from winning? With
wv and Approval they'll never have to reverse a preference in order to keep
Y from winning. Wilth IRV and Margins they'll sometimes have to bury their
favorite, vote someone over their favorite if they want to keep Y from
So methods like IRV and Margins illustrate that a shoddy rank-method is
worse than not using a rank-method.
I might ask you what good it does to guarantee that voting your favorite in
first place can't hurt your favorite, when you strategically need to bury
That criterion, the Weak Defensive Strategy Criterion, is a modest, minimal
thing that we'd expect of a method that honors majority rule and doesn't
have the worst form of the lesser-of-2-evils problem.
As I mentioned in an earier message, there are, with Margins and IRV,
situations (configurations of voters' preferences) in which the only Nash
equilibria are ones in which some voters vote someone over their favorite in
order to protect majority rule or to protect the win of a CW. But, with wv
and Approval, every situation has at least one Nash equilibrium in which no
one reverses a preference.
That's obviously a sense in which it can be accurately said that wv and
Approval are sincere methods and that Margins and IRV are not.
By the way, about LNH, I've probably already said this here, but the reason
why IRV doesn't let you lower preferences hurt your favorite is that IRV
eliminates your favorite before it lets you help your lower choices. IRV
saves your favorite from harm from lower preferences by eliminating your
favorite before letting you help your lower preferences. A sort of electoral
Someone said that because IRV doesn't let lower preferences hurt higher
ones, that means that IRV has no incentive for truncation. That isn't quite
so. Saying that lower preferences can't hurt higher ones isn't quite the
same as saying that adding more candidates to your ranking can't worsen the
outcome for you. As I said before, Professor Steven Brams published an
example refuting the claim that IRV never rewards truncation.
All four majority defensive strategy criteria measure for the popular
standards of majority rule and getting rid of the lesser-of-2-evils problem.
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