Meaningful votes

In the unlikely event that we get a second referendum on Brexit, here’s how it ought to be done: Arrange all the alternatives in a line in order of “hardness” of Brexit. In may be felt that Remain should not be an option, in which case we have Norway plus (a.k.a. Common Market 2.0) at one end, and no-deal at the other. Every voter chooses their favourite option from the list. The winning option is chosen to be the one for which at least half the voters prefer a harder Brexit, and at least half favour a softer Brexit. The claim that this system is truthful, is based on the presumed single-peaked-ness of preferences: every voter has a favourite option, and their support for the others goes down, the further away you get from the favoured option.

Of course, the only thing less likely than a second referendum is the adoption of an eminently sensible approach such as the one above, and the interesting question is, why it would not be used. One objection I can think of, goes as follows: suppose there are 3 alternatives offered, say Norway plus, Theresa May’s deal, and no-deal. Suppose that 20 million voters support Norway plus, another 20 million support no-deal, and one voter supports May’s deal. In that case, May’s deal wins, and someone would complain it’s (a lot) less popular than one of the others (probably the one the complainant supported). In reality, this result should have everyone — on both sides — celebrating the fact that whatever outcome they liked least has just been narrowly averted. A better objection is that some people would prefer a principled in-or-out result, and either extreme is preferable to some sort of fudge. (I admit, I recently heard that view sincerely expressed.) So, for them the vote is not truthful, but there are not many people like that, and they are free to vote (strategically) for whatever extreme they prefer. A third objection, implicit in most objections to electoral reform, states that voters are too stupid to understand anything other than plurality, or “first past the post”.

If the above system were used in Parliament, May’s deal would probably win, unless MPs were allowed to vote anonymously, in which case Norway Plus would probably win.

I checked the paper Thirteen Reasons Why the Vickrey-Clarke-Groves Process Is Not Practical since the point about voting is analogous to the observation that no-one uses VCG. The 13 reasons are mostly not applicable, or only weakly applicable, to the above election. It is true that there are other weak equilibria besides truth-telling, but it seems unlikely that someone would vote against his preference simply because he’s unlikely to swing the outcome.

The effort we put into studying voting systems is justified by the following Milton Friedman quote:

Only a crisis - actual or perceived - produces real change. When that crisis occurs, the actions that are taken depend on the ideas that are lying around. That, I believe, is our basic function: to develop alternatives to existing policies, to keep them alive and available until the politically impossible becomes the politically inevitable.

The will of the people

At one point in Iain Banks’ novel The Wasp Factory, the main character (a troubled teenager called Frank) makes the following observation:

Often I’ve thought of myself as a state; a country or, at the very least, a city.

He then compares his moods and thought processes to political moods that countries go through:

…For example, there has always been a part of me which has felt guilty about killing Blyth, Paul and Esmerelda. … But I liken it to an opposition party in a parliament, or a critical press; acting as a conscience and a brake, but not in power and unlikely to assume it.

Frank is modelling a single self-contained agent (himself) as the embodiment of many separate agents. It is common in literature for someone to have a struggle between, say, the admirable and the less admirable parts of his nature, but the above is the best example I can recall of this kind of modelling.

Usually we do the opposite, trying to represent many agents as a single one. In the context of Brexit, that approach has been stretched to breaking-point. The phrase “the will of the people” attempts to conflate the electorate (a multitude of agents) into a self-contained purposive entity. Is Brexit the will of the people? Yes, in the same sense that getting a hung parliament is the will of the people. The people seem to want to make life difficult for themselves. UK politicians and commentators have discussed negotiating Brexit with the European Union as if the EU is a self-contained purposive agent. This has led to the unfortunate idea that the EU may want to punish the UK for leaving, in order to discourage other states from leaving. It views the EU as a single entity motivated by the desire to survive and grow, and assumes that it will take actions that run counter to the goodwill of EU leaders. Likewise, we have recently heard a great deal about how Parliament has said what it doesn’t want, but not what it wants. If Parliament is modelled as a single agent, then it ought to want something, but as soon as we acknowledge that it’s not a single agent, there is no particular reason to suppose that there is something that it wants. Given, say, three alternatives, there could perfectly well be a Condorcet cycle.

Returning to Frank, it may be useful to model an individual as a multitude of internal agents. In economics, it could be a new an interesting way to model individual irrationality, which is a perennial challenge that has been taken up in a rather patchy way, and deserves more attention. Finally it may even constitute a way to model emotions: in Frank’s case it is guilt that is represented this way.