Ihor Kendiukhov

So you switch from your plan B to your current preference A. You are dynamically inconsistent.

A clever adversary who knows your preferences can now exploit this.

They offer you a sequence of trades.

Pay a small amount to switch from plan A to plan B before the coin flip because X ante you prefer B in context, then after the coin lands heads, pay a small amount to switch from B to A because X post you prefer A in isolation.

You have paid twice and ended up exactly where you started.

Subheading.

Dynamic consistency plus consequentialism.

Right arrow.

Independence.

This means independence is entailed by the conjunction of dynamic consistency and consequentialism.

It does not mean independence is the only way to avoid money pumps.

Dynamic consistency alone is what prevents exploitation, if you always follow through on your plans, no one can pump you by getting you to switch midstream.

And the Hammond result shows that dynamic consistency together with consequentialism implies independence, but this leaves open a crucial possibility.

What if you maintain dynamic consistency while giving up consequentialism?

In that case, you can violate independence and still be immune to money pumps.

The money pump relies on a specific sequence of events.

First, you form a plan.

Then, partway through, you deviate from it because your local evaluation at the intermediate node, which, under consequentialism, ignores the branches that didn't happen, differs from your global evaluation when you made the plan.

If you simply don't deviate, if you stick to your plan regardless of what your local preferences at intermediate nodes might suggest, the pump has no lever to pull.

The adversary offers you a trade midstream, you say no, I committed to a plan and I'm executing it, and the pump breaks down.