What kind of tax would a libertarian economist endorse?

Alex Tabarrok of Marginal Revolution writes today about the Arizona Voter Reward Act, which, if passed, would reward Arizona voters with a lottery ticket for a chance to win a million dollars.

Now I happen to agree with the USA Today editorial that Prof. Tabarrok links to:

[I]t's a tawdry idea. It cheapens one of the most important things a citizen of a democracy can do. It amounts to bribing citizens to vote. It reduces the act of voting to the equivalent of buying a Powerball ticket. It says it's less important to weigh candidates, and issues such as the war in Iraq, than to simply show up for a chance at the prize.

But that's not what bothers Prof. Tabarrok:

Frankly, too many people vote already. I know, that's heresy against the great religion of democracy - i.e. worship of the mob - but other people voting is an externality on me and in this case I will side with Pigou.

For those of you who don't know the economic jargon that Prof. Tabarrok uses, I'll explain.

In economics, an externality is an effect, positive or negative, that one's action have on another person, which one does not take (fully) into account when deciding whether or not to perform that action. Externalities are one of the things that can cause inefficiencies in a free market economy.

For example, by driving one produces both pollution and traffic congestion. Pollution and traffic congestion are negative externalities of driving. These effects on others are not fully taken into account by drivers, so we end up with more air pollution and traffic jams than the optimal amount (from an economic point of view).

Prof. Tabarrok is saying that voting is an action that has (negative) effects on others, and these effects are not fully taken into account by others. This leads to a more-than-optimal amount of voting.

Arthur Pigou was the economist who developed the economic concept of externalities. He also proposed a mechanism by which the market inefficiencies produced by externalities could be remedied: activities which have negative externalities, such as driving, can be taxed. (And activities that have positive externalities can be subsidized.) This causes actors to "internalize the externality," and so produce the optimal amount of the activity (from an economic point of view).

So what Prof. Tabarrok is endorsing is a poll tax, a tax on voting. Unfortunately for Prof. Tabarrok, the 24th amendment stands in the way of his preferred policy:

The right of citizens of the United States to vote in any primary or other election for President or Vice President, for electors for President or Vice President, or for Senator or Representative in Congress, shall not be denied or abridged by the United States or any state by reason of failure to pay any poll tax or other tax.

Do you suppose that Prof. Tabarrok (Canadian by birth) is unaware of the history of the poll tax in the U.S.?