[EM] Head to Head Comparison of Election Methods

[Blake Cretney]

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