[EM] Head to Head Comparison of Election Methods

[Michael A. Schoenfield]

At 09:43 PM 5/26/99 +0000, you wrote:
>Paul Dumais wrote:
>
>> I would like to propose a debate to compare my favorite election method
>> (I call it Dumais) and anyone else's favorite election method (for fun).
>> My goal is to discover which method is the best at fairly and
>> efficiently ranking candidates based a set of voters' choice(s). Though
>> I doubt any method will be universally accepted in every situation; I
>> think such a debate will bring interesting issues to light which may
>> alter people's views. I will take up this challenge with the first
>> serious challenger.
>> 	Here is a description of Dumais voting.
>> 1.  Each voter ranks one or more of the available candidates.
>> 2.  Do a standard borda count.
>> 3.  Divide the candidates into two groups. One group (the preferred
>> group) all have a Borda Count (BC) of BC > (C-1)*V/2 where C is the
>> number of candidates and V is the number of voters. The second group
>> (the non-preferred group) has BC < (C-1)*V/2.
>> 4.  Repeat steps 2 and 3 (on the preferred group) until the preferred
>> group is small enough to choose the winner or winners. A complete
>> ranking of all candidates can also be done in this way by repeating
>> steps 2 and 3 on each group.
>> 
>> Unranked choices split the remaining borda count (or (U-1)/2 where U is
>> the number of unranked candidates). This method can be interpreted in
>> another way. Each candidate gets one point for every opponent it defeats
>> on a single ranking by a single voter. Each candidate gets 1/2 point for
>> each opponent it ties with (unranked candidates). The borda count is
>> equivalent to asking: "how many times does a candidate (ie A) defeat
>> another candiate when we compare him to every other candidate using all
>> the available information (ie using each voter's ranking of the
>> candidates)?". Elimination is required to reduce the effect of
>> introducing identical candidates (as a stratategy) and to allow us to
>> reduce the effect of "lower" candidates in our choice of the best
>> candidate. A borda count in the only fair way to choose candidates for
>> elimination, since it is the only method that takes into account all of
>> the voting information without predjudice.
>
>What do you mean by "without prejudice?"
>
>Also, I do not agree that Borda uses all the voting information.  For
>example, Borda's method of totalling renders these two blocks of
>voters
>30 A B C
>30 B C A
>30 C A B
>
>and,
>
>30 A C B
>30 B A C
>30 C B A
>
>as equivalent.  That may or may not be a good thing, but it points
>out the fact that Borda ignores certain kinds of information.  Of
>course, this is true of all methods.
>
>You seem to believe that the fact your method uses Borda is a selling
>point.  I view the use of Borda to be a fatal flaw in your method. 
>The problem with Borda is that it allows the same information to be
>re-used.  
>
>For example, if candidate X loses to candidate Y, the method uses
>this as evidence against candidate X.  Fair enough.  But if two
>candidates Y1, and Y2 are both in the running, and are identical in
>the mind of voters, it will follow that X will lose to both by the
>same margin.  So the information, that a certain majority of voters
>prefers a candidate like Y to one like X, is essentially counted
>twice.
>
>As a result, Dumais suffers from vote-splitting (as demonstrated in
>my previous email on the subject), although not to the same extent as
>plurality.  This means that the more candidates there are representing
>an ideology, the more likely it is to lose.
>
>This is a serious problem for its own sake.  However, I see it as
>particularly unfortunate because this is not a problem in IRV.  If we,
>as Condorcet advocates, propose Dumais, IRV advocates will point this
>failing out.
>
>This is one of the reasons I advocate Path Voting (which seems to
>have been invented by Markus).  If you have a path from one candidate
>to another, like the following from A to D:
>
>A has a majority over B of 19 votes
>B has a majority over C of 20 votes
>C has a majority over D of 18 votes
>
>we measure the path's strength by its smallest majority, in this case
>18.  A will be ranked above D unless D has an even greater path back
>to A (strength measured by smallest majority).
>
>So, for a simple case
>40 A B C
>35 B C A
>25 C A B
>
>A>B 65-35=30
>So, A has a path to B of strength 30.
>B's best path to A is
>B>C 75-25=50, C>A 60-40=20
>giving a strength of 20.  So A will be ranked above B.
>
>A>B [30] B>C [50]
>So, A has a beat path to C of strength 30.
>C's best path to A has strength 20, so A will be ranked above C.
>
>Looking further we have B...>C [50] and C...>B [20], so B is ranked
>above C.
>
>So, A B C is the complete ranking.  In this case the same as Dumais.
>
>Can you give an example where you think the Path Voting result is
>inferior to that given by Dumais?
>
>> 
>> This voting method meets the Smith criterion, condorcet criterion, and
>> reverse-consistancy.
>
>So does this one.
>
>> 
>> -- 
>> Paul Dumais
>> 
>---
>Blake Cretney
>
>=======================================================================
Blake and Paul,

I would love to take both of you on, but unfortunately I am not aware of
any modeling of the Socio-Psychological Model put forth by the Michigan
School. If you are aware of any specific modeling, I would certainly
appreciate any leads.


Michael S.

Michael Schoenfield
Michael A. Schoenfield & Associates, Ltd.
2637 Mason Street
Madison, WI 53705-3709

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