One of the reasons put forward by some conservatives for voting for the controversial Republican nominee is that not voting for him would be “a vote for Hillary”. It’s important to understand why this is a *really bad argument*.

In the first place, the claim itself is inaccurate. If there are only two candidates, A and B, and Oscar doesn’t vote for A, that could mean one of two things:

(1) Oscar votes for B rather than A.

(2) Oscar votes for neither A nor B.

Clearly these aren’t equivalent, because (1) hinders A’s chances of winning more than (2) does.

But it’s worse than that: the reasoning here is incoherent, because if a non-vote for A is a vote for B, then by parity of reasoning a non-vote for B is a vote for A, from which it follows that *not voting for either candidate* is *voting for both candidates*. On the most charitable interpretation, that simply means not voting at all would be *neutral* with respect to the candidates: it wouldn’t favor either of them. On a less charitable interpretation, it’s just a nonsensical conclusion.

Perhaps there are some good reasons for conservatives to cast their vote for the Republican presidential ticket in 2016, but this isn’t one of them.

**Addendum:** I should add that the same incoherence afflicts another popular argument, namely, that not voting would “allow Hillary to win”. If a non-vote for A would allow B to win, then equally a non-vote for B would allow A to win, in which case not voting for either candidate would allow both candidates to win, which is absurd. (Actually, the conclusion in this case could be interpreted somewhat more charitably: not voting would allow *either* candidate to win. But again this just highlights the *neutrality* of a non-vote.)

Brian BosseHello Dr. Anderson,

There may be a more charitable way to think about this argument; namely, allow for the unstated premise:

(Assumed Premise)If Oscar votes, then he will vote for candidate B.Let’s say that candidate A has ‘x’ votes and candidate B has ‘y’ votes prior to Oscar’s vote/non-vote. A’s lead is equal to (x-y). Once again, we are faced with two scenarios:

(1)Oscar votes.(2)Oscar does not vote.If Oscar votes, then A’s lead over B would become (x-y-1) given the assumed premise above. Let’s label A’s lead in this scenario ‘L’, i.e., L = (x-y-1). Therefore, if Oscar votes, then A’s lead equals L. If Oscar does not vote, then A’s lead equals (L+1). In

thissense, a non-vote by Oscar islikea vote for A. I suspect something like this is what is intended by those who put forth such arguments. Is this reading too charitable?Kind Regards,

Brian

JamesThanks for this thoughtful response, Brian. Frankly, I doubt that’s what is intended by most of those who make the “not voting for B is voting for A” argument (it’s too thoughtful!) but perhaps

somehave something like that in mind. However, I see two problems:1. It still doesn’t show that not voting for B is

equivalentto a vote for A. Let’s grant the assumed premise and the argument that Oscar’s not voting for B would result in a lead of (L+1) for A. Given the very same assumptions, Oscar’s voting for A would result in a lead of (L+2) for A. Soat mostone could say that Oscar’s not voting for B amounts to “a half-vote for A”. But then it would still be misleading to suggest that not voting for Bisa vote for A.2. I think the assumed premise is rather presumptuous because it presupposes that voting for B is really a “live option” for Oscar, i.e., that he has no overriding reasons for not voting for B. The assumed premise is really a subjunctive conditional: If Oscar

wereto vote, then hewouldvote for B. But the truth-value of that counterfactual is quite disputable, because perhaps Oscar finds his circumstances to be such that he simply cannot vote for either candidate. Thus the antecedent of the conditional is an empty hypothetical. So I think this argument assumes something about Oscar that he might well dispute (e.g., if Oscar is by conviction a “Never B-er”).Brian BosseHello Dr. Anderson,

Thank you for responding to me. I suggested above that

mostpeople who make these types of arguments assume something along the lines of theassumed premiseabove. You doubt this, but allow thatsomemay have this in mind. Nevertheless, you believe this still falls short in that “…at most… Oscar’s not voting for B amounts to ‘a half-vote for A’”. Your argument for this seems to be along these lines:_______________________________________

Rebuttal ArgumentIf Oscar does not vote for B, then A’s lead is either L+1 or L+2. The lead difference between these two alternatives is 1. Assuming these are two real possibilities, then Oscar’s not voting for B amounts to a 1/2 vote for A.

_______________________________________

I think there is problem with this argument; namely, the two “possibilities” are not real possibilities. The

assumed premiseprecludes Oscar from voting for A; so, A’s lead cannot be L+2. If Oscar does not vote for B, then the only alternative is that he does not vote at all. This would result in A’s lead increasing from L to L+1. Again, it is inthissense that a no-vote for Oscar islikea vote for A.Now, it is possible that the Rebuttal Argument misrepresents the argument you actually made. If so, could you clarify your argument for me? Thank you so much for your consideration.

Sincerely,

Brian

JamesHey Brian,

Actually, I offered three arguments against your proposal. But since you focus here on the first, I’ll do likewise. You suggest my argument is problematic because I treat Oscar’s voting for A as a “real possibility,” but that isn’t the case, and thus the L+2 scenario should be discounted. Leaving aside the issue of what exactly counts as a “real possibility,” I’ll simply observe that whether or not Oscar’s voting for A is a real possibility is irrelevant to my argument. The original claim was that not voting for B

isa vote for A. I take that to be an equivalence claim. But if so, it’s strictly false, because Oscar’s voting for A would result in a lead for A greater than if Oscar were not to vote. Whether Oscar’s voting for A is a real possibility is neither here nor there; we still know what Oscar’s voting for A would entail, and that would not be equivalent to Oscar’s not voting at all. It’s a simple point of mathematics. So my argument doesn’t assume that the L+1 and L+2 scenarios are real possibilities, because that’s irrelevant to the argument.Now, perhaps your response will be that the original claim is not an equivalence claim but a similarity claim. It’s not that Oscar’s not voting

is equal toa vote for A, but rather than Oscar’s not votingis likea vote for A. Well, how much like it?Halflike it? :)My other two arguments were objections to the assumed premise. In fact, the second one amounted to the idea that Oscar’s voting for B might be no more of a “real possibility” than Oscar’s voting for A. In that case, once again, by parity of reasoning, the claim that Oscar’s voting for A isn’t a real possibility won’t do the argument-defeating work it has been conscripted to do.

Brian BosseHello Dr. Anderson,

I am afraid I have done a poor job explaining myself. Please forgive me for testing your patience as I try to make my argument as perspicuous as possible in this response. Consider the following three premises:

(1)Oscar votes if and only if Oscar votes for either candidate A or candidate B.(2)Oscar does not vote for both candidates.(3)If Oscar votes, then Oscar votes for candidate B.Premises (1) and (2) simply limit the possible candidates Oscar can vote for to either A or B, but not both. Premise (3) is the added assumption that I originally proposed. Now, the question I am asking is what follows from these three premises? (Note: whether or not any of these premises are true is irrelevant at this point. I am simply asking what would follow

ifthey were all true.) The answer is: Oscar either votes for B or not at all. Given this disjunction, it follows that A’s lead will be either L or L+1. From here, it is easy to see that:(4)If Oscar does not vote, then A’s lead will be one more than it would be if Oscar does vote.Now consider the following statement:

(5)A no-vote by Oscar is a vote for A.Here is my claim:

(BC)If what is meant by (5) is (4), then (5) is a reasonable argument.I claim that (4) is tautologically entailed by (1), (2) and (3). If this is the case, then assuming that

tautological entailmentis reasonable, (BC) is established. Do you agree?This leads to the next question: Does (4) express what is really meant by (5)? Now, I grant that a no-vote by Oscar is not

equivalentto a vote for A. But couldn’t (5) in the right context simply be a rhetorical device used to express (4)? If so, then (5) in itself does not necessarily express an equivalence claim. I will stop here.Kind Regards,

Brian

JamesHi Brian,

You’re not testing my patience at all. It’s a pleasure to interact with someone who cares about clarity and precision. Sorry about the delay in replying; first-week-of-semester busyness is to blame.

We can certainly agree on this: (4) follows from (1-3), and

if(5) is understood as equivalent to (4)then(5) must follow from (1-3) as well. No room for dispute there.My objections then come to this: first, (3) may be a gratuitous and disputable assumption (esp. in the current political context) for some of the people to whom the argument is directed; and second, even allowing for rhetorical devices, (5) is a very misleading and prejudicial way to express (4). Taken at face value, (5) has entailments that (4) does not. In my view, statements like “A non-vote for B is a vote for A” rely far more on rhetorical force than logical force to persuade people. And I take exception to that!

By the way, my blog is currently set up to close comments after 30 days. If you’d like to post a reply (and you’re welcome to have the last word!) just email it to me, or send it via the contact form on the About page, and I’ll gladly post it on your behalf.

JamesOne further criticism of that line of argument is that it treats votes and non-votes merely as quantitative contributions to a candidate’s final tally, ignoring the qualitative properties of a vote. Specifically, it overlooks the fact that a vote has an intrinsic expressive meaning independent of its quantitative contribution. See this post by Lydia McGrew for some discussion.