[EM] LNH, Mono-Add-Top, etc

MIKE OSSIPOFF nkklrp at hotmail.com
Sun Dec 28 21:54:02 PST 2003

Someone posted:

"Mono-add-top" is a Woodall criterion which says that adding ballots that 
all give
first-preference to X must not harm X. It is met by IRV and Margins, but not 
by WV.

I reply:

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 
majorilty rule.

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 
your favorite.

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.

Mike Ossipoff

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