Letter to the Guardian Published Friday, 26 November
2004
Dear Sir/Madam,
So, the Commons is to have a free vote on
several majority votes on various options. This means that,
in theory, the MPs can vote in favour of more than one option.
Indeed, on the Today programme (27th Feb), Chris Bryant MP
suggested that Jack Straw may well vote in favour of his first
three preferences: 50%, 60% and 80% elected. Obviously, in
his (Straw’s) opinion, all three of these options are
better than the status quo. But what happens if lots of MPs
behave like this?
Imagine a debate on just five options: option
A (all appointed), B (80%/20%), C (50/50), D (20/80) and E
(all elected). And let us assume that, in a parliament of
100 MPs, their preferences are as follows:
Preferences Number of MPs
18 19 20 21 22
1st preference A B C D E
2nd preference B A D C D
3rd preference C C B E C
4th preference D D A B B
5th preference E E E A A
Well, in majority voting, if every MP votes
in favour of only their 1st preference, the results will be:
A 18, B 19, C 20, D 21 and E 22; in which case, nothing gets
a majority, {but E would win if the count was conducted as
in a plurality vote (which is like first-past-the-post)}.
If all the MPs vote in favour of both their
1st and 2nd preferences, the results will be: A 37, B 37,
C 41, D 63 and E 22, so D will win with a majority of 63.
If, as Jack Straw might, they all vote in
favour of their 1st, 2nd and 3rd preferences, the results
will be A 37, B 57, C 100, D 63 and E 43, so there will be
three winners, with majorities in favour of B, C and D of
57, 100 and 63%, respectively.
Finally, if everyone votes for their 1st,
2nd, 3rd and 4th preferences, the results will be A 57, B
100, C 100, D 100 and E 43, which means there will be four
winners, with majorities in favour of A, B, C and D of 57,
100, 100 and 100%, respectively.
In a word, “The proposed voting procedure”
of a series of majority votes “is the daftest,”
to quote Lord Desai, speaking in the debate four years ago,
(Hansard, 22.1.2003).
How much wiser it would be if parliament were
to follow the same Lord’s advice and use a “rankings”
system, i.e., a Borda count, so to identify that option which
has the best average preference. In the above example of five
options, the best possible average preference score is 1,
(which is what an option gets if everyone gives it a 1st preference);
the worst possible score is 5 (which is what an option gets
if everyone gives it their last or 5th preference); and the
mean score is 3. Now in any contest, something will always
be above the mean, and something else below; a Borda count
will always give a definite result.
In our own example, the average preference
scores of the five options are: A 3.51, B 2.87, C 2.39, D
2.53 and E 3.70, so the winner is option C with the best average
preference score of 2.39; (and option D is the runner-up,
with an average preference of 2.53).
Yours sincerely,
Peter Emerson
Director, The de Borda Institute
www.deborda.org
OurKingdom, the new economics foundation and the de Borda Institute recently gave interested parties from think tanks, research groups and campaigning organisations, and members of the general public, the opportunity to participate in an online trial of consensus decision making.
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