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On the right we see the preference ordering.
We use Pi to denote voter i's preference ordering over X.
Here, two of the three people have the same strict preference ordering.
Kaplow and Shavell include the agent's moral concerns in this extended preference ordering.
It also provides a natural preference ordering on explanations, defined in terms of normality or plausibility.
The first condition says that for any combination of individual preferences, the rule should yield a collective preference ordering.
Call an ordering that incorporates every consideration that the agent views as relevant to her decision "an extended preference ordering".
Savage's representation theorem gives strong results: starting with a preference ordering alone, we can find a single probability function, and a narrow class of utility functions, which represent that preference ordering.
Each expected utility function determines a unique utility function over outcomes, as well as a unique preference ordering.
This step thus incorporates within the agent's preference ordering anything that the agent considers relevant to her decisions.
One therefore cannot expect that agents in all cases do come up with a transitive and complete preference ordering.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com