Number of Ballots First Choice Second Choice
18 A C
12 C A
10 C A
9 C A
4 C A
2 C ASo C survives by a vote of 37 to 18.- Numerical total. We’ll assume that the rule here is 5 points for a first-
place vote, 4 points for a second-place vote, and so on. You don’t have
to spend time hauling out the calculator. I’ll do it for you. The result
is that D wins this contest, with 191 5 9 4 18 3 (12 4 2)
2 10 points. - Head-to-head matchups. You can probably see this one coming. E
wins all head-to-head matchups. He or she beats A by 37 to 18, B by 33
to 22, C by 36 to 19, and D by 28 to 27.
Each of the previous methods has liabilities, and the prior example
helps to illustrate what these liabilities are. If we use the most first-place
votes to determine the winner, we may end up with someone who is pre-
ferred by a small minority and loathed by the majority. If we use the run-
off method, it is possible for someone who has almost a clear majority of
first-place votes to lose to someone who has an insignificant number of
first-place votes. The Survivor method may result in a winner who is
clearly preferred to only one of the candidates, who just happens to be the
other candidate left when it comes down to a two-person race. The nu-
merical totals method may yield different results depending upon the
scoring: a 7-5-3-2-1 scoring system weights first-place votes more heavily
than does a 5-4-3-2-1 scoring system. Finally, head-to-head matchups may
result in a winner whom the fewest voters feel has the qualities of a
leader.
This example has obviously been carefully tweaked: D wins the numeri-
cal total by a small amount, and E barely beats D in the head-to-head
matchup. Nevertheless, it becomes obvious that in a hotly contested elec-
tion, the result depends not only on the ballots that were cast, but also on
the method for determining the winner. We’re back to the question posed
at the start of this chapter: Is there a best voting method for determining
the outcome of an election?
Imagine for a moment that an election consultant is shown the results
Cracks in the Foundation 213