The agent is allowed to ask it’s submodules how they would feel about various gambles e.g. “Would you prefer B or a 50% probability of A and a 50% probability of C”. Equipped with this extra information a voting paradox can be avoided. This is because the preferences over gambles tell you not just which order the submodule would rank the candidates in, but quantitatively how much it cares about each of them.
Assuming the submodules are rational (which they had better be if we want the overall agent to be rational) then their preferences over gambles can be expressed as a utility function on the outcomes. So then the main agent can make its utility function a weighted sum of theirs. This avoids non-transitivity.
A preference order which says just what order the candidates come in is called an “ordinal utility function”.
A utility function that actually describes the relative values of the candidates is a “cardinal utility function”.
The agent is allowed to ask it’s submodules how they would feel about various gambles e.g. “Would you prefer B or a 50% probability of A and a 50% probability of C”. Equipped with this extra information a voting paradox can be avoided. This is because the preferences over gambles tell you not just which order the submodule would rank the candidates in, but quantitatively how much it cares about each of them.
Assuming the submodules are rational (which they had better be if we want the overall agent to be rational) then their preferences over gambles can be expressed as a utility function on the outcomes. So then the main agent can make its utility function a weighted sum of theirs. This avoids non-transitivity.
A preference order which says just what order the candidates come in is called an “ordinal utility function”.
A utility function that actually describes the relative values of the candidates is a “cardinal utility function”.