Borda Count

[LAYTON Craig]

Yes, the first one.

In relation to Borda, I remember an experiment we did in 1st year political
science, where all the students voted on the same thing (I think it was
chocolate bars).  We used a number of voting systems, and had to vote
sincerely and consistently across all the systems. The voting systems were;
first past the post, IRV, approval, borda and a rating system (out of 100).
The voting pattern was really interesting (there were two dominant factions,
one larger but more ambivalent, and the other smaller and more committed to
their candidate, and the members of a faction voted almost exactly the same
way, without prior communication on how to vote), but, anyway, all the
systems produced nearly the same result, except for borda, which produced a
wildly different result (out of six candidates, the candidate who won the
borda count came third in the rating system, and did even worse in some of
the others).

I thought it was quite interesting.

-----Original Message-----
From: Forest Simmons [mailto:fsimmons at pcc.edu]
Sent: Thursday, 1 February 2001 14:58
To: election-methods-list at eskimo.com
Subject: Re:Borda Count

Suppose you have 16 candidates to rank.  You know how each of them stands
on the four issues that you consider vital.  No two have the same profile
on these issues, so if we represent "agrees with you" and "disagrees with
you" by the letters a and d respectively, the 16 candidates can be
identified by their profiles:  aaaa, aaad, aada, aadd, adaa, adad, adda,
addd, daaa, daad, dada, dadd, ddaa, ddad, ddda, dddd

In an informal non-binding poll you are asked to rate them on a scale of
zero to 100%, so naturally you rate them in proportion to the number of
issues on which they agree with you (assuming all of the issues are
equally important to you).

aaaa gets 100%
addd, dadd, ddad, ddda get identical ratings of 75%
aadd, adad, adda, daad, dada, ddaa get identical ratings of 50%
daaa, adaa, aada, aaad  get identiacl ratings of 25%
dddd gets 0% .

Next, in another informal non-binding poll you are asked to rank the
candidates.

Since you cannot distinguish all of them on the issues, you use looks and
personality to break up the groups with identical ratings:

aaaa > aaad > aada > ... > dddd

The second pollster immediately converts your rankings to a rating via the
Borda Count with  rates between 0/15 and 15/15.

Which would you consider to be a more accurate representation of your
estimation of the candidates' abilities to represent your viewpoint in
the legislature? 

Forest