We are all single-issue voters

One of the things I love about social choice theory is the radical perspective on politics afforded when you regard democracy not as a moral duty or pragmatic arrangement, but as a map from a set of votes to a set of winners. We can then ask, what properties might we like this map to have, and what additional constraints are imposed on the map by those properties? If the map cannot simultaneously have every property we would like to impose, which should we regard as the most important to preserve? Is some map preferable in a special case than the one we prefer for the general case? All the psychology and morality are taken out, but the questions still feel so human.

Consider, for example, the abstract from a paper by Marcus Pivato, “Variable-population voting rules”:

Let X be a set of social alternatives, and let V be a set of ‘votes’ or ‘signals’. (We do not assume any structure on X or V.) A variable population voting rule F takes any number of anonymous votes drawn from V as input, and produces a nonempty subset of X as output. The rule F satisfies reinforcement if, whenever two disjoint sets of voters independently select some subset Y in X, the union of these two sets will also select Y. We show that F satisfies reinforcement if and only if F is a balance rule. If F satisfies a form of neutrality, then F satisfies reinforcement if and only if F is a scoring rule (which scores taking values in an abstract linearly ordered abelian group R); this generalizes a result of Myerson (1995).

So given very general assumptions about the properties of a voting system, we can conclude that each vote must correspond to a “score” awarded to each candidate, and the candidate with the best score wins. In our familiar first-past-the-post system, a vote’s first choice gets a score of 1 and other candidates get zero. But curiously, these scores don’t even need to be real numbers, as long as they’re drawn from a linearly ordered abelian group.

[As an example of a slightly weird linearly ordered abelian group, consider the following: let (G,+,<) be an ordered group under addition such that elements of G are points (x,y) in the Cartesian plane, added as vectors so that if a = (u,v) and b = (x,y), then a + b = (u+x, v+y). We then order these points as follows: a < b when (v < y) or (v = y and u < x). Using “scores” drawn from this group would amount to giving each candidate a real-valued score, with a separate real-valued score serving as a tie-breaker. Such a system would have the peculiar property that if candidate A were preferred by a single person along the first axis — in other words, his total score were (1,0) — then a candidate preferred by arbitrarily many people along the second axis — i.e., his score is (0, n) for any finite n — would still lose the election. Or to say the same thing in gratuitous math jargon, (G,+,<) is not Archimedean.]

This abstraction calls forth the same beautiful, spiritual feeling to me as the fact that in 1891–2000 human generations after the first known cave art around 38,000 BCE–it was finally proved that there are only 17 ways of tiling a wall with geometric patterns. (As far as I know, the Alhambra constructed in the 13th century is the only place on earth where all 17 groups were used, and even this is debated.) In the mathematical treatment, we take something we feel instinctively and go farther than intuition alone could ever lead us.

Things get really exciting in social choice theory when you include voters in the mix. For example, the McKelvey-Schofield “chaos theorem” tells us that an agenda setter can move the status quo from any position in policy space to any other by introducing a clever sequence of majority-rule referenda. As always, this theorem only holds under some reasonable-sounding assumptions, including that voters cast their votes according to their sincere preference at each referendum. On the other hand, the Gibbard-Satterthwaite theorem tells us that any reasonable voting system that uses voters’ preference orderings of candidates–a class of systems less general than Pivato’s “scoring rules” but still encompassing a lot more than just majority rule–will sometimes incentivize voters to cast a dishonest vote. The real-life applicability of the chaos theorem is dubious for this reason alone.

A particularly important social choice result is the “median voter theorem,” which states that–assuming candidates are aligned on a left-right spectrum and a voter casts their vote for the candidate whose policy alignment is closest to their own–the candidate preferred by the “median” voter (in terms of position along the left-right spectrum) will win. It is, of course, difficult to rigorously assign a “coordinate” on the left-right axis to every candidate and voter, so the utility of this theorem, too, is limited. That said, many positions are almost inexplicably coupled (e.g., knowing only someone’s views on gay marriage gives you substantial information about their probable views on the minimum wage), so the single-axis model is not as bad as it might be in a more rational world.

Thinking about these things is just so much more fun than studying real-world politics that it’s hard to resist looking at the state of the union with math-tinted goggles. But the truth is that the assumptions we can conveniently make about voter behavior gives voters–or mathematicians; I’m not sure–too much credit. At the end of the day, the electorate doesn’t look like a set of rational agents minimizing their single-parameter cost functions.

This is all a completely irrelevant (but to me, rather interesting) way of arriving at the question, how do we actually decide who to vote for?

In the 2016 presidential election, it seems to come down to a single question: Is this person Trump? Or for others: Is this person Clinton? That is, if you ask a Clinton supporter “what is the least dramatic thing that Trump would have to change before you threw your support to him,” I fear the answer is no less than “being Trump”; and likewise for Trump supporters about Clinton. How does this happen?

Obvious answers along the lines of “tribalism” might go most of the way to the truth, but the evolution of my own views this election cycle illustrates the point I want to make, with the added benefit of helping you decide how much I’m over-generalizing from my own example.

I was initially extremely reticent to vote for Clinton because of the mishandling of her e-mail server–and, despite the fact that this bears on less than 0.001% of policy space, I was reticent for that reason alone. This seems almost insane. But on some level, I still feel that decision-making process was the right one. If Trump were not so abhorrent, I would probably still be opposed to a Clinton presidency.*

What first swayed me to oppose Trump in all events was the exchange at the March 3rd Republican debate in which he defended his promise to give military orders that violate international law.**

At neither decision point did I weigh the issues on both sides and find anything resembling a preponderance of evidence favoring one candidate over the other. There does, of course, exist a preponderance of evidence favoring one candidate; no two candidates are “equally bad” as it is sometimes claimed. It’s just that I can’t handle optimizing over a policy space in more than two or three dimensions–and I’m not sure I can even handle that much. So I ignore most of the nuance and take the position demanded by some “principle” (in other words, a reduction of the policy space to a mere binary).

It’s hard to say “I’ll reconsider if Clinton turns out to be cleared of all wrongdoing regarding her e-mail server,” or “I’ll reconsider if Trump reverses his position on giving illegal orders.” Maybe it feels too petty, or too vulnerable to manipulation from the other side. Whatever the cause, we soon find ourselves saying “Clinton/Trump is so terrible that I can’t even begin to enumerate the reasons.” The single-issue decision takes on a more dramatic character without actually managing to be about more than one thing.

In the past, I’ve found it difficult to understand how people came to harbor so much hatred for McCain or Romney, or for Obama. But perhaps the opposition that starts with an opinion on gay marriage or government-mandated healthcare just feeds on reinforcing evidence until the flimsiness of its original foundation is securely hidden. No one wants to pin the future of their democracy on a thirty-second debate response.

When we sweep the bulk of the issues under the rug to make our decision easier, normally the quality of discourse suffers but we might usually end up in about the same place. Only once in a blue moon, we will have someone whose appeal along their most favorable axis is totally at odds with their fitness for office viewed holistically. Trump is such a person. Many people will cast a Republican vote this election in good faith based on some single issue, whether that’s Clinton’s record of transparency, concern about uncontrolled immigration, outsourcing of jobs, a feeling of disenfranchisement by establishment politics, or the impression that Trump is less likely to engage in military conflicts without a pressing national interest. But the American people don’t get a line-item veto on the activities of the executive branch. If we bargain for just one thing, then we shouldn’t be surprised when we get more than we bargained for.

*Despite the FBI’s recommendation against criminal charges, Clinton’s handling of the e-mail scandal has been shameful, as has been the left’s characterization of the entire issue as a distraction manufactured by the right. Her campaign web site still says “No information in Clinton’s emails was marked classified at the time she sent or received them.” Contrast this with Director Comey’s statements that “From the group of 30,000 e-mails returned to the State Department, 110 e-mails in 52 e-mail chains have been determined by the owning agency to contain classified information at the time they were sent or received. Eight of those chains contained information that was Top Secret at the time they were sent; 36 chains contained Secret information at the time; and eight contained Confidential information, which is the lowest level of classification.”

More incriminating details from the same statement:

“With respect to the thousands of e-mails we found that were not among those produced to State, agencies have concluded that three of those were classified at the time they were sent or received, one at the Secret level and two at the Confidential level.”

“It is also likely that there are other work-related e-mails that they did not produce to State and that we did not find elsewhere, and that are now gone because they deleted all e-mails they did not return to State, and the lawyers cleaned their devices in such a way as to preclude complete forensic recovery.”

“Although we did not find clear evidence that Secretary Clinton or her colleagues intended to violate laws governing the handling of classified information, there is evidence that they were extremely careless in their handling of very sensitive, highly classified information.

For example, seven e-mail chains concern matters that were classified at the Top Secret/Special Access Program level when they were sent and received. These chains involved Secretary Clinton both sending e-mails about those matters and receiving e-mails from others about the same matters. There is evidence to support a conclusion that any reasonable person in Secretary Clinton’s position, or in the position of those government employees with whom she was corresponding about these matters, should have known that an unclassified system was no place for that conversation.”

“With respect to potential computer intrusion by hostile actors, we did not find direct evidence that Secretary Clinton’s personal e-mail domain, in its various configurations since 2009, was successfully hacked. But, given the nature of the system and of the actors potentially involved, we assess that we would be unlikely to see such direct evidence. We do assess that hostile actors gained access to the private commercial e-mail accounts of people with whom Secretary Clinton was in regular contact from her personal account. We also assess that Secretary Clinton’s use of a personal e-mail domain was both known by a large number of people and readily apparent. She also used her personal e-mail extensively while outside the United States, including sending and receiving work-related e-mails in the territory of sophisticated adversaries. Given that combination of factors, we assess it is possible that hostile actors gained access to Secretary Clinton’s personal e-mail account.”


BAIER: Mr. Trump, just yesterday, almost 100 foreign policy experts signed on to an open letter refusing to support you, saying your embracing expansive use of torture is inexcusable. General Michael Hayden, former CIA director, NSA director, and other experts have said that when you asked the U.S. military to carry out some of your campaign promises, specifically targeting terrorists’ families, and also the use of interrogation methods more extreme than waterboarding, the military will refuse because they’ve been trained to turn down and refuse illegal orders.
So what would you do, as commander-in-chief, if the U.S. military refused to carry out those orders?

TRUMP: They won’t refuse. They’re not going to refuse me. Believe me.

BAIER: But they’re illegal.

TRUMP: Let me just tell you, you look at the Middle East. They’re chopping off heads. They’re chopping off the heads of Christians and anybody else that happens to be in the way. They’re drowning people in steel cages. And he — now we’re talking about waterboarding.

This really started with Ted, a question was asked of Ted last — two debates ago about waterboarding. And Ted was, you know, having a hard time with that question, to be totally honest with you. They then came to me, what do you think of waterboarding? I said it’s fine. And if we want to go stronger, I’d go stronger, too, because, frankly…


… that’s the way I feel. Can you imagine — can you imagine these people, these animals over in the Middle East, that chop off heads, sitting around talking and seeing that we’re having a hard problem with waterboarding? We should go for waterboarding and we should go tougher than waterboarding. That’s my opinion.

BAIER: But targeting terrorists’ families?


TRUMP: And — and — and — I’m a leader. I’m a leader. I’ve always been a leader. I’ve never had any problem leading people. If I say do it, they’re going to do it. That’s what leadership is all about.

BAIER: Even targeting terrorists’ families?

TRUMP: Well, look, you know, when a family flies into the World Trade Center, a man flies into the World Trade Center, and his family gets sent back to where they were going — and I think most of you know where they went — and, by the way, it wasn’t Iraq — but they went back to a certain territory, they knew what was happening. The wife knew exactly what was happening.

They left two days early, with respect to the World Trade Center, and they went back to where they went, and they watched their husband on television flying into the World Trade Center, flying into the Pentagon, and probably trying to fly into the White House, except we had some very, very brave souls on that third plane. All right?


BAIER: Senator Cruz, you were mentioned.

TRUMP: I have no problem with it.

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