Suppose
you are confronted in the US Presidential election with precisely three
candidates (with no option for a write-in, just because). You find both
Candidates A and B, the two favorites, such that you cannot cast your vote for
them, and you are trying to figure out whether you should vote for Candidate C
or just refrain from voting altogether. You’ve been told both that a vote for C
is a vote for A, and a vote for C is a vote for B; you’ve also been told that a
lack of vote is a vote for A, and a lack of vote is a vote for B. Suppose you
want to find out what the best strategy is: to vote for C, who will almost
assuredly not win, or not vote at all, to register your displeasure at the
system, to retain your moral integrity, because you’re apathetic, or any
combination of these.

Conveniently,
in our stipulated story, there are only 99 voters in your state (whew, now

*that’s*low turnout!). Also convenient is the fact that you know that Candidate A has received 50 votes (50.5%), Candidate B has received 48 votes (48.5%), and Candidate C has received 1 vote (1.01%)[1]. Consider the following four scenarios:**1.**

**You vote for Candidate A.**

This
has the effect of

*increasing*A to 51%,*decreasing*B to 48%, and*decreasing*C to 1%. Your*actual*impact on the election is minimal, given that A wins whether you vote for A or refrain from voting at all.[2]**2.**

**You vote for Candidate B.**

This has the effect of

*decreasing*A to 50%,*increasing*B to 49%, and*decreasing*C to 1%. Your*actual*impact on the election is minimal, given that A wins whether you vote for B or refrain from voting at all.**3.**

**You refrain from voting at all.**

This has the effect of

*maintaining*A, B, and C. Your*actual*impact on the election is not known, given how we’re using “actual impact” and the fact we haven’t investigated C yet.**4.**

**You vote for Candidate C.**

This has the effect of

*decreasing*A to 50%,*decreasing*B to 48%, and*increasing*C to 2%. Your*actual*impact on the election is minimal, given that A wins whether you vote for C or refrain from voting at all.
Here,
then, is the upshot: if you cannot in good conscience vote for A or B, then in
terms of sheer outcome (winner), it doesn’t matter, given the parameters,
whether you vote at all. But if you want to vote your conscience, voting for C
has the effect of registering your disapproval of A and B (by decreasing their
share of the vote) while also registering your approval of C [edited for coherence] (by increasing C’s
share). So, kids: in this type of a case, math supports you.[3]

[1] I have clearly rounded each
of these numbers.

[2] Here, I am using “actual
impact” to differentiate between only two options: voting for a particular
candidate or not at all. It’s just a way of keeping track between the two
strategies, and I wanted to show A’s and B’s significance in the whole thing. I
also recognize that the relative percentages A and B may have in the real world
can vary: I’m really just investigating this type of situation (and
sufficiently similar ones).

[3] I realize, of course, that
there are other, principled reasons to vote for a third-party candidate or not
at all. I just thought this was a neat way, in relevant cases, to choose
between the two options.