|
Voting and Mathematics:
There is no way to guarantee a
'fair' election when 3 or more choices are presented to two or more voters.
Read on to learn why!
A mathematician dude named Arrow proved (as in there is no way around it)
that the statement above is true. This proof has become known as
Arrow's Impossibility Theorem. To do this, he made several basic
assumptions that seem to be very sensible. Those assumptions are:
1) Universality (the vote must have a result)
2) Non-imposition (every ranking of candidates must be
possible...no cheatin/hankypanky stuff)
3) Non-dictatorship (one person's opinions can't force a
candidate's ranking)
4) Monotonicity (one candidate can't be hurt by including a new option
unless society prefers the new candidate)
5) Independence of irrelevant outcomes (if one candidate is removed,
ranking of the other candidates should not change)
(These seem like pretty reasonable assumptions,
ya?)
Let's look at what happened in the '00 presidential election by
looking at the "The Nadar Effect"
1) The vote was universal (there was a result...in order, Bush,
Gore, Nadar)
2) Non-Imposed (let's forget the counting fiasco in Florida and assume that
the Florida results really did reflect the will of the people)
3) Non-dictatorial (folks could have voted for whomever they
wanted)
So far, the election seems like it was fair...HOWEVER...
4) Monotonicity: What if Perot had been in the mix?
Would that have taken enough votes from bush so that the new order would have
been, perhaps,
Gore, Bush, Perot, Nadar? (note: Perot's place is irrelevant...the
thing that is not fair is that Gore jumps over bush in this instance)
5) Independence: What if Nadar had been abducted by aliens who (in)conveniently
erased his name from all ballots? Would the new order have become Gore
then Bush? Quite likely!
It is likely (or at least POSSIBLE) that the suggested reorderings in 4) and 5)
would have occurred. It is for this reason, that our method of electing
a president is demonstrably unfair.
That being said,
"democracy is the worst form of government except for all those others that have
been tried." -- Winston Churchill
All we can do is
Key info is paraphrased/quoted/etc from -->
here
<--
|