I have a new voting proposal.

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Arrow's theorem shows that a voting system that follows simultaneously a set of conditions defined by it is impossible. A simplistic interpretation is that we can't have a completely fair voting system when there are more than 2 choices. But that's just the simplistic interpretation.

It does not show that the current method is the fairest possible.

By fairest possible you mean the least unfair. Either an election process is perfectly fair or it is unfair. Unfairness can be ranked by degree, I suppose. So an election that is not perfectly fair is unfair.

Aside from simple two outcome races the fairest elections are no elections at all.

ruveyn

You are free to like the current method and to believe it is the least unfair or the most fair (same thing really). Just don't base that opinion on Archer's theorem.

Quite right, dictatorship is the way to go!

Just because total success is impossible doesn't mean one should strive for partial success. Whether one should say that a system is the "least unfair" or the "most fair" is irrelevant. The point is, some give more representative results than others.

East Germany had elections.

You probably could have a dictatorship that was relatively liberal and open as well. It needn't be like the worst examples of the Twentieth Century. Doesn't necessarily mean it'll be good though.

But I am not indifferent to the outcome. I am very much interested in the outcome, but I have been deprived of a choice on an arbitrary basis.

With runoff elections, preferential ballots or STV, at least the disappearance of my candidate of choice is based upon a broader electoral concensus. But in your "pick one of two" scenario, there is no such legitimacy for the two options that make it to the ballot.

Consider the Australian republice referendum. That referendum provided only two choices: the status quo or selection of a president by a two-thirds majority of Parliament. What was a person who believed in a directly elected head of state to do? (In a jurisdiction with compulsory voting, no less). The result was a preservation of the monarchy when polling numbers suggest that a majority of Australians would prefer a Republican form of government. By skewing the options, the result likely defied the majority opinion on the substantive question.

The Arrow theorem fails to acknowledge that a choice between two options is an invalid choice if there are more than two options that could be available to a decision maker.

Then you are talking about a choice process with more than two choices and one outcome which Arrow proved to be unfair.

It is as he proved.

ruveyn

Then Arrow's theorem only applies to votes on ONE choice. There is always the option not to vote for anything, and a null choice is still a choice. Two candidates represents at least three voting options (more if you include, say, fielding a third candidate).

That was not my point ruveyn, and you know it.

My point is that Arrow failed to also demonstrate that a two choice option is just as unfair as any system to multiple options, because the reduction to two choices is arbitrary and artificial.

That is because reality is complex in practice, not because of a failure in Arrow's theorem.

You are quite correct.

The failure is actually ruveyn's in attempting to establish Arrow's theorem as in any way relevant to elections and referenda as they are undertaken today.