Margins Example final part

David Marsay djmarsay at
Wed Sep 23 09:16:19 PDT 1998

The following is an important example that still awaits a response.

> From:          Mike Ositoff <ntk at>
> Subject:       Margins Example final part
> Date:          Sat, 19 Sep 1998 16:44:55 -0700 (PDT)

I have changed it slightly as Mike's alignments don't work for me. I
hope I've interpreted correctly. If not, it is still an important

> 100 voters.
> Sincere preferences:
41 A(BC)
39 B(AC)
20 BCA
(where braces denote a tie)
> Actual votes (A voters insincerely order B & C):
41 ACB
39 B(AC)
20 BCA

> With Margins, A voters' strategy succeeds, & A wins.

I have previously posted: 
Subject:          Re: Margins Example Continued
Date sent:        Mon, 21 Sep 1998 11:24:03

Here I suggested that we should focus on spatial voting, since 
tactical voting problems are unavoidable in the general case.

Mike kindly replied off-line:
>All of my examples for Votes-Against vs Margins have been
>spatial examples, with a 1-dimensional policy-space or
>political spectrum.

For a spatial interpretation of Mike's example:
Options can be ordered with B or C in the middle, but not A (else CBA
is non-spatial). Then we suppose that the supporters of A and B are
blind to the space.

I propose a more spatial example, with B in the middle of A, C.

12 ABC
10 BAC
8   CBA

B is the Condorcet winner (CW).
Now, suppose those who prefer A actually vote A(BC). Then one has a 
cycle of pluralities. If one takes plurality as 'for-against' then 
the Condorcet tie-breaker discounts AB to give A as the winner. Note 
that C cannot defend against this. Thus it seems a 
sensible way for A to vote. The danger would be if C gained support, 
in which case C might win.

More generally, if there were one large extreme party and many minor 
parties, one might expect the large party's supporters not to 
declare their preferences.

I haven't understood the 'votes against' proposal yet. I propose a 
'votes-for' tie-breaker. Maybe its the same in the end, though.
I suggest that where there is a cycle, we discount the link that has 
the least votes-for support.

Suppose we have A,B,C as before.
Let a, b,c denote the number of voters who prefer A,B,C respectively.
Let ba, bc denote those who prefer b first and a (resp. c) second.
Let |XY| denote the pairwise support For 'X > Y'.

Then |BA| = b + c, and |CB| = c, so for b > 0, |BA| > |CA|.

Note that A's supporters do not contribute to these, and could only 
do so by voting C ahead of B. Hence |BA| will not be discounted by a 
'votes-for' tie-break.

I don't know if this brings any other problems. For now, I wonder how 
we might rationalise it.

Using 'margins' is equivalent to using a Young/Kemeny distance that 
has a tie (AB) half way between AB and BA. This fits Dodgson too.
The idea is to minimize the conflict between a voter's ranking and 
our overall ranking. 'Votes-for' seems to only take account of 
explicit rankings. Thus a tie is treated as 'do not mind' rather than 
'half way between the two.'

Is 'votes-against' really the same, or does it have a similar 


Sorry folks, but apparently I have to do this. :-(
The views expressed above are entirely those of the writer
and do not represent the views, policy or understanding of
any other person or official body.

More information about the Election-Methods mailing list