[EM] RE: a better Bucklin flavored FBC satisfying method

Simmons, Forest simmonfo at up.edu
Tue Sep 27 16:05:33 PDT 2005



From: election-methods-electorama.com-bounces at electorama.com on behalf of election-methods-electorama.com-request at electorama.com
Sent: Sun 9/25/2005 12:00 PM
To: election-methods-electorama.com at electorama.com
Subject: Election-methods Digest, Vol 15, Issue 53


I had written ..

> Note that in ordinary Bucklin the ordinal information below the eventual stopping level is
> wasted.  It doesn't matter if four levels or fifty levels are allowed, only the information in
> the top two or three levels ever gets used, since almost all voters will put one of the two
> front runners somewhere in the top two levels.
> This new method remedies that.  Although it collapses ordinal information in the top few ranks
> in order to find a level at which not all candidates are majority defeated, it doesn't waste the
> remaining ordinal information.

Kevin replied  ...

However, you get an opposite problem: Information regarding "irrelevant"
candidates (those with majority defeats) can affect who wins. This is why I
don't feel that MAMPO ("Majority Approval, Minimum Pairwise Opposition") is
clearly better than MDDA. (Both satisfy FBC, SFC, and SDSC.)

Forest replies...

Irrelevant?  I think that weak candidates can expose weaknesses in strong candidates.  If two strong candidates are equal in all other respects, I would say that the weaker one is the one who has the most trouble fending off a weak candidate.


Kevin went on ...

Also, the MMPO component is huge. MMPO's failure example for the plurality criterion
still works in your method:

1000 A
1 A=C
1 B=C
1000 B

C wins.

I reply ..

I think that this problem is easily remedied by using the power truncation version of MMPO.

Note that when MMPO with power truncation is restricted to only two slots, it always gives the same result as Approval.

Of course, if we throw in power truncation, then we have to say what we mean by majority defeat.  Do we mean majority defeat with or majority defeat without power truncation?  I say without, since otherwise we might collapse down to two levels and still have every candidate with a majority defeat.


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