Computer scientist Leslie Lamport formalized the paradox as
“Buridan’s Principle,” which states that the ass will starve if it is situated
in a range of possibilities that include midpoints where two opposing forces
are equal and it must choose in a sufficiently short time span. We assume,
based on a principle of physical continuity, that the larger the bale of hay
compared to the other, the faster will the ass be able to decide. Since this is
true on the left and on the right, at the midpoint, where the bales are equal,
symmetry requires an infinite decision time. Conclusion: within some range of bale
comparisons, the ass will require decision time greater than a given bounded
time interval. (For rigorous treatment, see

*Buridan’s Principle*(1984).)
Buridan’s Principle is counterintuitive, as Lamport
discovered when he first tried to publish. Among the objections to Buridan’s Principle
summarized by Lamport, the main objection provides an insight about the source
of the mind-projection fallacy, which treats probability as a feature of the
world. The most common objection is that when the agent can’t decide it may use
a default metarule. Lamport points out this substitutes another decision
subject to the same limits: the agent must decide that it can’t decide. My
point differs from that of Lamport, who proves that binary decisions in the
face of continuous inputs are unavoidable and that with minimal assumptions
they preclude deciding in bounded time; whereas I draw a stronger conclusion:
no decision is substitutable when you adhere strictly to the problem’s
conditions specifying that the agent be equally balanced between the options. Any
inclination to substitute a different decision is a bias toward making the
decision that the substitute decision entails. In the simplest variant, the ass
may use the rule: turn left when you can’t decide, potentially entrapping it in
the limbo between deciding whether it can’t decide. If the ass has a metarule resolving conflicts to favor the left, it has an
extraneous bias.

Lamport’s analysis discerns a kind of physical law; mine
elucidates the origins of the mind-projection fallacy. What’s psychologically telling
is that the most common metarule is to decide at random. But if by random we
mean only apparently random, the strategy still doesn’t free the ass from its
straightjacket. If it flips a coin, an agent is, in fact, biased toward
whatever the coin will dictate,

*bias*, here, means an inclination to use means causally connected with a certain outcome, but the coin flip’s apparent randomness is due to our ignorance of microconditions; truly random responding would allow the agent to circumvent the paradox’s conditions.**The theory that the agent might use a random strategy expresses the intuition that the agent could turn either way. It seems a route to where the opposites of functioning according to physical law and acting “freely” in perceived self-interest are reconciled.**
This false reconciliation comes through confusing two kinds
of symmetry: the epistemic symmetry of “chance” events and the dynamic symmetry
in the Buridan’s ass paradox. If you flip a coin, the symmetry of the coin
(along with your lack of control over the flip) is what makes your reasons for
preferring heads and tails equivalent, justifying assigning each the same
probability. We encounter another symmetry with Buridan’s ass, where we also
have the same reason to think the ass will turn in either direction. Since the
intuition of “free will” precludes impossible decisions, we construe our
epistemic uncertainty as describing a decision that’s possible but

*inherently*uncertain.
When we conceive of the ass as a purely physical process subject to two opposite forces (which, of
course, it is), then it’s obvious that the ass can be “stuck.” What miscues
intuition is that the ass need not be confined to one decision rule. But if by
hypothesis it is confined to one rule, the rule may preclude decision. This
hypothetical is made relevant by the necessity of there being

*some*ultimate decision rule.**The intuitive physics of an agent that can’t get stuck entails: a) two equal forces act on an object producing an equilibrium; b) without breaking the equilibrium, an additional natural law is added specifying that the ass will turn. Rather than conclude this is impossible, intuition “resolves” the contradiction through conceiving that the ass will go in each direction half the time: the probability of either course is deemed .5. Confusion of kinds of symmetry, fueled by the intuition of free will, makes Buridan’s Principle counter-intuitive and objective probabilities intuitive.**

How do we know that reality can’t be like this intuitive
physics? We know because realizing

*a*and*b*would mean that the physical forces involved don’t vary continuously. It would make an exception, a kind of singularity, of the midpoint.