[EM] How good can a method be?

MIKE OSSIPOFF nkklrp at hotmail.com
Fri Jan 16 01:57:02 PST 2004

>3. If more than 1 remain, apply Approval, electing the candidate above the
>most voters' Approval cutoffs.

You wrote:

>Chris Benham's suggestion would make sense here: any ballots that approve
>all or none of the remaining candidates could be minimally adjusted to
>make them relevant in step 3.

Absolutely. That hadn't occurred to me, but of course it should be done.

Smith Majority Approval meets wv's majority defensive strategy criteria, 
while reducing other strategy incentives.

To meet those criteria with a pairwise-count method results in some 
that are unavoidable for a good pairwise-count method. So I was interested 
in finding other, nonpairwise-count ways of meeting those critreria, to 
reduce those strategy needs.

Smith-Majority-Approval, though not entirely pairwise-count, is still mostly 
pairwise-count (finding the Schwartz set and majority defeats). For that 
reason it doesn't entirely get rid of those strategy incentives, but it does 
reduce them.

Pairwise-count, with its accompanying additional minor strategy incentives, 
is probably the only way to meet the majority defensive strategy criteria 
with a method as simple as wv or Smith Majority Approval.

NES & DSV (batchwise and ballot-by-ballot) of course are not pairwise-count 
methods. It's pretty much a sure thing that NES meets the majority defensive 
strategy criteria, and I expect that DSV does also. So those are methods 
that share wv's defensive strategy properties, but without the other 
strategy incentives that are unavoidable when meeting those criteria with a 
pairwise-count method.

Though we on EM initially discussed offensive truncation, offensive 
order-reversal, and defensive truncation as wv strategies, it turns out that 
those are strategy possibilities that are present with all the best methods, 
including wv, and anything  better that is found. The defensive strategy 
situation of wv can't be improved on. It will be the same with any best 
1-balloting method.

It's always been a matter of how good a voting system can be. How much it's 
possible to improve on wv. Very little, it turns out. A few unimportant 
extra strategy incentives can be gotten rid of.

Apparently NES, and probably DSV too, are the ideal methods. Ideal because 
they reduce strategy to its irreducible minimum.

How good can a method get? As good as NES & DSV.

Now, what pairwise-count strategy incentives am I referring to? Well, in the 
wv vs margins debates, it was pointed out that, with wv, there can be 
incentive to rank several of one's favorite candidates equally in 1st place, 
even if one has perferences between them. For instance, if you believe, as I 
do, that the candidates can be divided into 2 sets, such that the merit 
differences within the 2 sets are negligibe compared to the merit difference 
between the sets, then, with wv, it's to your advantage to rank all the 
better-set candidates equally in 1st place. That's how I'd vote in a wv 

I'm not criticizing wv. It's the best method (or class of methods) that's 
been thoroughly studied & discussed. And what very little improvement on it 
is possible is not possible with a comparably simple method.

I still advocate wv as the rank-count method to propose. SSD, MAM, or PC. It 
probably isn't time to propose the fancier completely ideal rank-counts, 
even if they'd been thoroughly studied & discussed. Maybe sometime later, 
after wv has been in use, someone could eventually suggest a more 
complicated ideal method.

The margins advocate who pointed out that strategy incentive seemed to 
consider it a big problem. But I replied that it's only a strategy 
"incentive", and not a defensive strategy need. No one needs to equal-rank 
in order to protect majority rule or to protect the win of a CW. The only 
situations in which a voter could benefit by the equal ranking would be in 
certain special kinds of natural circular ties. So not only is it not a 
defensive strategy need, but it isn't even an important incentive.

Most won't have incentive to do other than sincerely rank the candidates. 
That's because most people don't seem to agree with me about those 2 sets. 
(One way I word it is to say that the election has one or more completely 
unacceptable candidates who could win). So, for instance, most progressives 
won't feel that strategy incentive, and will feel free to sincerely rank the 
candidates. Nader, Sharpton, Kucinich, Dean, [& the rest of the Democrats], 
in order of preference, where I'd vote Nader & Sharpton in 1st place.

But, even for me, who'd vote according to that incentive in wv, I don't 
consider it a problem. After all, the reason I'd vote that way is precisely 
because I consider the better-set candidates relatively
uniform in merit.

Basically, I'd be using Condorcet as Approval. An Approval ballot perfectly 
expresses the preferences of someone who consideres there to be just 2 
merit-levels. And it quite adequately expresses the preferences of me, who 
consider 2 merit levels to be the imiportant distinction.

The other wv strategy incentive that the margins advocates mentioned is even 
less important:

If you have no preferences among your lower choices, wv gives you incentive 
to randomly rank them, in order to give them more votes-against. It isn't 
quite clear to whom that's supposed to be a problem. To the person who is 
indifferent between those lower choices?

Not a problem. But, in any case, NES & DSV get rid of that unimportant 
strategy incentive too.

Of course it isn't entirely true that, with wv, one should rank all the 
candidates. That's because, with any method, even the best methods, 
defensive truncation can be needed in order to deter offensive 
order-reversal, if the electorate is sufficiently devious.

I hesitated to bring these subjects up,  lest I make it sound as if wv has a 
problem. I emphasize that wv's extra strategy incentives are nothing 
compared to margins' unnecessary drastic defensive strategly needs, or those 
of IRV. With wv there's no need for defensvie strategy unless someone is 
attempting offensive strategy. That can't be said of margins or IRV.

I also hesitated to bring all this up because I was afraid that I'd restart 
the wv vs margins debate.

But the topic of how good a method can be is interesting, and it requires 
mentioning certain trivial, minor, unimportant, but avoidable strategy 
incentives of the best simple rank-counts, the best rank-counts currently 
being proposed, the wv methods.

Mike Ossipoff

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