[EM] 3Ballot -- Condorcet version #2

[mrouse1 at mrouse.com]

I was playing with the ThreeBallot method some more today, and I realized
you could make my previous Condorcet suggestion far more secure by
converting the rank list to pairwise comparisons. Let's assume you have a
computerized voting booth -- since the method is much more difficult with
just pen and paper -- and a strict preference of candidates ABC such that
A>B>C.

Inputting A>B>C into the computer would give the pair comparisons
A>B
A>C
B>C

Let's assume this is put into the first column. Then let's mirror this in
column 2 and put the reverse in column 3. You would have

Col1    Col2    Col3
A>B     A>B     B>A
A>C     A>C     C>A
B>C     B>C     C>B

(hope the spacing stayed okay on that side).

Now, randomly swap pairs between columns:

Col1    Col2    Col3
A>B     A>B     B>A
A>C     C>A     A>C
C>B     B>C     B>C

(Since there are only three candidates, no order is going to look *that*
random, but with four or more candidates you could really mix things up).

Now, let the voter pick whatever column he or she wants as a record.
Looking in isolation, Column A appears to be a vote for A>C>B, Column B
looks like a circular tie, and Column C looks like a vote for B>A>C. None
of these possibilities give much of a clue about the true order A>B>C.
With a large enough pool of voters, it would be practically impossible to
pick even one particular order, and simply having that order wouldn't say
anything about the actual vote. If you wanted, you could also allow ties
both in the voter column and the randomized pairs, I just ignored it to
make an easier example. I think this method could also be used for Borda
(simply give a point for each win), though I don't really care for that
method despite Donald Saari's preference (heh).

Anyway, if someone sees a problem with it or think of something else, let
me know. I'm going to play around with converting Plurality/Approval to
pairwise comparisons and see if there is a way around mask the actual vote
(to make it harder to buy) without making it too difficult for the voter
to understand and compare in the voting booth.

Michael Rouse
mrouse1 at mrouse.com