People who favour democracy
should wish for votes to translate into MPs, but alas, as things stand the constituency
boundaries currently favour Labour and disadvantage the Conservatives, because they
are not of equal size, and because Tory votes are often heavily concentrated in
safe seat areas.
The proposal to reform the
boundaries was blocked by the Lib-Dems in coalition a couple of years ago - a
reform that would have seen the number of MPs reduced to 600, and the constituency
boundaries being of roughly equal size, making the political outcome much more
representative as the Conservatives would have gained between 20 and 25 extra
MPs. Until those boundary changes occur, the people of Great Britain
Not only does percentage of votes
not translate consistently into number of seats - number of seats doesn't translate
into voting power either. At the low end there is no direct link between a
party's influence and its number of votes.
Imagine a reduced parliament in
which there are only 120 MPs. The
Conservatives have 50, Labour has 40, The Lib Dems have 20 and UKIP has 10.
Despite Labour having twice the number of MPs as The Lib Dems, a coalition
between The Conservatives and The Lib Dems would give them a majority, and give
Labour less power than a party that obtained half their MPs. There are a vast
number of inter-party permutations for coalitions, meaning that a party with
relatively few votes can be nearly as powerful as a major party in a coalition,
or equally pretty much powerless, depending on how the land of the coalitions
lies.
While we're in the mood
for oddities - some of you may have heard of Kenneth Arrow's 'impossibility theorem', which proves that an aggregation of society's individual preferences doesn't translate into a comprehensive aggregate societal preference. Let me try and break it down this way. Imagine the three big leaders are running for a national
popularity contest, and observe the strange goings on that occur here. Let us
say that a third of the electorate prefers Ed Miliband( M ) to Nick CKlegg
( K ) to David Cameron ( C ), another third of the electorate prefers K to C to
M; and the remaining third prefers C to M to K. There is nothing particularly
strange about this until we consider what happens in two person contests given
the above preferences.. M can boast that two-thirds of the electorate prefers
him to K. C responds that two-thirds of the electorate prefer him to M.
Finally, K counters by noting that two-thirds of the electorate prefers him to
C.
In mathematics, a binary
relation over a set is transitive if whenever an element a is related to an element b,
and b is in turn related to an
element c, then a is also related to c. If
the societal preferences in what I’ve just said are determined by majority
vote, we have an irrational ordering of preferences; that is, ‘society’ prefers
M over K, K over C, and C over M. Thus even if the preferences of all the
individual voters are transitive (by that I mean that transitivity holds if,
wherever a voter prefers Cameron to Miliband and Miliband to Clegg, he or she
prefers Cameron to Clegg), the societal preferences determined by the majority
vote are not necessarily transitive and thus not necessarily rational either.
Kenneth Arrow's
theorem demonstrates that given the foregoing all reasonable voting
systems (or equivalently, economic market systems) are subject to such
irrationalities.
Let me try
to posit some further clarity with a different illustration. Think of our three
leaders M, K, and C as cars rather than people, and then think of a woman
deciding which of the three cars to buy. Let’s give her three criteria
(interchangeable and commensurate with one another) for making this decision;
looks, affordability and performance. Car M looked better than car K, which
looked better than car C. On the other hand, car K was more affordable than car
C, which in turn was more affordable than car G. Finally, car C performed
better than car M, which performed better than car K.
Since the woman placed
equal and commensurate measure on each of these criteria, she would be in a bit
of quandary here. She clearly preferred car G to car K (M outscored K on two
criteria). She also preferred car K to car C (for the same reason) - yet she
preferred car C to car M. And if you are following here you will see that the
same problem of non-transitivity holds for individuals, and that when broadened
out to an election it leaves a bit of a detritus. In the case above one only
need induce the woman to declare one of the criteria more important than the
others. This is easier than convincing one third of the electorate to change
its mind.
Given the foregoing; there
are four conditions under which consistency will show that we cannot derive
societal preferences from individual preferences…
1) The societal
preferences must be transitive (if society prefers x to y and y to z then it
must prefer x to z)
2) The societal
preferences must satisfy the principle - if alternative x is preferred to
alternative y by a majority in the society, then society must prefer x to y.
3) The societal
preferences must satisfy the independence of irrelevant alternatives (the
societal preference depends only on the orderings of the individuals with
respect to alternatives in that environment).
4) The societal
preferences must not be susceptible to autocracy - there is no individual whose
preferences automatically determine all of society’s preferences.
As for the realities of
the electoral situation, of course we know that the political portrait of
lucidity has been gravely disfigured from the bottom up as much as the top
down, so the absolute best that one can hope for is that through the
media-manipulating smokescreen the impressionability and cognitive indigence
does not wholly impair the view of those gazing in, and that in the absence of
a good rationale people’s gut instincts amount to enough in seeing who is very
evidently the least bad party for the job - at least in the next few years.
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