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"Logical decision theory" is a new family of decision theories, of varying levels of formalization, which are argued to have key implications for theories of economic rationality, the design of sufficiently advanced machine intelligence algorithms, and of course the philosophy of rational decision. Logical decision theories impinge on whether it's rational to vote in elections, or rational to give in to blackmail, or how computational agents should play in dilemmas if the agents have common knowledge of each others' source code.

The new idea in logical decision theories can glossed as "choose as though you were choosing the logical output of your decision algorithm".

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An economic standpoint. Please start by telling me how this is relevant to economically rational agents deciding whether to vote in elections.
A computer science or Artificial Intelligence standpoint. Start by talking to me about programs and code.
The standpoint of analytic philosophy. Talk to me about Newcomblike problems and why this new decision theory is better than a dozen other contenders.
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Normal algebra is fine. Please be careful about how you toss around large formulas full of Greek letters.
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Guide to Logical Decision Theory