# Arrow's Theorem and Buridan's Ass

1. Jul 10, 2006

Staff Emeritus
Michael Nielsen has a good discussion of Arrow's Theorem:

A dictator means here that in spite of having a large number of voters ranking the alternatives, there is just one whose ranking matches the final ranking implemented, using any fair (according to the hypotheses of the theorem) voting system whatsoever. see Nielsen's post for the reasons we conclude this.

And it occurred to me that this can account for the supposed paradox of Buridan's Ass. You recall that this says that an ass equidistant from two bales of hay will starve to death because (Being a robotic zombie in Jean Buridan's philosophy) it has no sufficient reason to prefer going to one rather than the other.

But the ass actually has three choices; it can go to bale A, or to bale B, or it can ignore both bales. Suppose now that the ass's robotic brane is built on the basis of Dennet's Conscieusness Explained (surely even dualists will grant me this in the case of a zombie). This theory features competing agents each with an agenda to sell to their collectivity - in other words a voting scheme, and in this case each agenda is a preference ranking of the three choices, and Arrow's theorem should apply. So not alll agents are equal and one, just one, of them determines the action of the collectivity in spite of their independence. So there is no effective vote, but rather a single dictatorial agenda - whatever it is - is implemented. The ass survives.

And what does this then say about Dennet's scheme in general?

Last edited: Jul 10, 2006
2. Jul 10, 2006

### loseyourname

Staff Emeritus
This would depend on the features of the voting system. Restating the theorem again:

Dennett's competing agents would have to vote in a manner that 1) ranks alternatives relative to each other, rather than simply casting a yes vote for one alternative, 2) respect unanimity, and 3) respect the independence of independent alternatives. I don't recall Dennett laying out the method by which his agents vote in this degree of specificity; in particular, though I would assume that 2 applies, 1 and 3 are not at all so clear.

I can actually think of one other issue in applying this to Buridan's Ass Paradox. Given that the dilemma is contingent upon the agent (in this case, the entire ass) not being able to decide between two equally appealing options, it would also seem to apply to any sub-agents that might collectively make a decision for the entire organism. To put it another way, if we take the paradox to present a dilemma upon which a decision cannot be made, then no votes would even be cast.