So, from our election here, let’s find
the winner using the plurality method. The plurality method is probably what
you’re most familiar with. It is the idea that We’re only going to
look at people’s first choice. We’re going to ignore everything else.
and we’re going to look at which choice, or which candidate, got the highest
number of first choice votes. Now the, this is a slightly dfferent than
majority rules, because majority implies 50% more than 50% is a majority.
When we have more than 2 options it’s quite common that none of the choices get
50% of the votes. So notice here that A, got four first
choice votes. One here and three here.
Or, O here got three, first choice votes and Hawii got three first choice votes.
So the winner under. Plurality method is A.
Notice that this is however it’s 4 votes out of 10 is 40% so this is not a
majority, this is what’s called a plurality and hence the plurality method.
Now, the plurality method is, you know, fairly well known and very easy to do.
So, so, what’s the issue with it? So, let’s talk about Condorcet winners.
so Condorcet was looked at voting and, and, we’re going to look at preferences
if there is only two choices. So, let’s compare A versus
A versus O. So if it was a versus , these people
would prefer A. These people would prefer A.
These people would prefer O. These people would prefer A.
Now, remember, we’re ignoring H as an option.
So A would have one, two, three, four, five, six, seven people liking A, whereas
O only has three people preferring it over Over the other option.
Now again we’re looking at 1 1 on 1 comparison here.
So in this in this comparison a would be the preferred choice.
If we look at a versus h, then let’s see. A is preferred, a is preferred, h is
preferred, h is preferred, so four people prefer a and six people prefer h and so h
would be the preferred choice there. How about o versus h.
so if we look at o versus h o is preferred here, h is preferred here, o.
And H, so we have one, two, three, I’m sorry, one and three is four people
preferring O, and six people preferring H, so H is preferred.
So, notice something really interesting here, H is preferred, by the majority.
so H is preferred by the majority. I suppose I should spell that right.
Preferred by the majority over A and is preferred over O.
If, if those were the only options and yet.
Our winner under plurality method is A. So the co, so in this case because H is
preferred over all other candidates, we call H, we call H the Condorcet winner or
the Condorcet candidate. and in this case plurality method did not
choose the Condorcet winner. Now not every election has one, but this
one does. And so this is what we call a violation
of a fairness criteria, and this is called the Condorcet criteria.
it says that if there’s a condorcet winner, they should win or, more
appropriately, it would be fair if they win and, plurality is not doing that.
So that suggests that plurality is not a particularly fair method for voting.