Hmm. The article is technically correct but irrelevant. The case where necessity fails relies on three conditions: (1) the number of voters is even (2) the number of voters is small (3) at least one voter has their optimal preferences exactly identical to the proposed equilibrium; not merely 'very close' but exactly. All three (plus some additional, complicated conditions) must hold for Plott's conditions to be sufficient but not necessary.

(2) is obviously not a concern here, for nation-state electorates. (3) is implausible: just introduce a suitably fine-grained continuum of possible policies. If you still have an ideal voter at the equilibrium, it's not fine-grained enough.

On (3), in particular: in general, mainstream economics ignores degenerate cases in utilitarian analysis. That's why the additional conditions are not mentioned: it requires that of a (finite) number of voter ideal points, at least one of them must fall on the equilibrium. But in a multidimensional phase space, the set of equilibrium points is a set of measure zero! Why would you care about that case?

Note: "the MVT is a good empirical first approximation" is not the same as "the MVT is a good predictor of politician behaviour".

This is because of two things: first, the MVT does not necessarily hold when issues are multidimensional. Plott (1967)'s AER article demonstrates that when voter preferences are multidimensional, then the requirements for a stable majority vote to exist at all are quite stringent and unlikely to obtain in reality. The usual voting problem issues crop up. The winner is ultimately the agenda-setter, who can control the final vote and therefore the outcome.

It is however true that most contemporary issues are observed to align along a single axis. But this is the second issue: the more true the MVT is as an empirical first approximation, the more similar politicians will be, and the more they will need some way to distinguish themselves from their competitors! All that the MVT tells you is that over the vast majority of the policy possibility space, politicians will have similar views. And so they do. We could fund programs to search for the Lost City of R'lyeh, but we don't, etc.

Because politicians are so similar over the vast majority of the space, the gains from introducing additional dimensions for voters to puzzle over are potentially enormous. All they need to do is introduce a single issue which breaks the pairwise symmetry of the existing median-voter-favoured equilibrium - some issue where the degree to which people care is deeply asymmetric. If it 'sticks', then they are assured of a victory. If it doesn't, then all you've lost is some advertising budget.

So that's what politicians do: they try to find issues which, at least for a while, don't align cleanly along the predominant axis. Most issues won't stick, because the possibility space is enormous.

It would apply if gold were legally enforced and usable as a currency, but I don't think it is.

It does apply to forex speculation, though.

Well, no. Concisely put, the problem is under-determined money demand because of readily available money or money-like substitutes (in the theoretical framework of money demand/money supply). This is an issue limited to the period of readily available new money, of which Bitcoin itself is one, really. For those thousands of years there were few such substitutes, and substitution would have been costly anyway, so the problem does not apply there.

That's not the analog; the analog would be the externality effect. An individual lowering (excessively high) prices imposes a loss on themselves but creates a positive externality on all other individuals; since the externality is never internalized, price adjustment is underprovided. If price adjustment is costly, the problem is even worse.

Wages are not thought to be sticky for this reason (real wages are not as obviously anticyclical as the argument would imply.).

Has anybody seen any reply to Tyler Cowen's argument that Bitcoin's monetary velocity is unstable?

The arguments I have encountered focus on Bitcoins' strengths as a medium of exchange, but not (as Cowen points out) as a store of value, as one currency among a monetary universe composed of many money-like substitutes. Why hold non-negligible amounts of Bitcoin (as opposed to cash for its state-enforced liquidity, or any less-liquid but higher-return financial instrument of choice - recall Fisher's equation here)?

The mainstream Keynesians like to talk up liquidity preference. The post-Keynesians and modern monetary theory types talk about fiat money demand as driven by the state (to pay taxes, etc.). Well, Bitcoin cannot do that, either - it is fiat money without a fiat. We know all about Bitcoin's stable money supply. What determines its money demand? Demand for anonymous money? But the supply of anonymous-money-substitutes is not limited to Bitcoin.

(An alternative way to phrase the problem, via a standard result from international macro - flexible exchange rates and high rates of currency substitution imply unstable exchange rates; the more perfect and costless the substitution, the more unstable the exchange rate, with the rate becoming indeterminate as cost goes to zero. This is the point made by the paper Cowen mentions. Currencies in use in the world tend to correlate remarkably well with geopolitical boundaries, regardless of whatever optimal currency areas that may exist, for reasons that have less to do with their intrinsic economic properties than with state measures; states have central banks and central banks can defend currencies, so the problem presented by rampant currency substitution is really only limited to weak states in military turmoil. Bitcoin is another matter, though - it doesn't suffer any of the vagaries of bad central banking, but it can't claim any of the strengths either.)

edit: "unstable exchange rates" is not quite clear. "Exchange rates highly elastic to changes in money demand and supply" might be better.