If trade is permitted, and there are no transaction costs, all outcomes are pareto optimal. That’s what I was objecting to.
I think you might be worried more about maximizing expected (or average) utility than pareto optimization. The two are largely unrelated.
Again, I may be misunderstanding something, but the requirement that there be a universal scale for utility seems to require that individuals be interchangeable, if the scale is dependent on observable characteristics (e.g. someone who has $200 has 2 utils of happiness). Unless this scale is somehow contingent on measuring subjective utility, you’re saying that pareto optimality should be possible only when players have an agreed-upon set of preferences.
Even if I’m confused on that point, I still fail to see how this hypothetical relates to anything in reality.
If people are Pareto optimal in a trade, then yes, that trade is Pareto optimal.
However if there are three trades between three people (12, 23 and 31) and each trade is Pareto-optimal, that does not mean that the set of three trades as a whole is Pareto-optimal. It’s generally possible to change these trades and get a better outcome for everyone (which is kinda what a market with price signals tries to do).
The only cases where you cannot do this is precisely where there is an agreed upon weighting of everyone’s utility function etc...
The individuals need not be interchangeable, the weighting need not be fair. But Pareto-optimality is only possible in this situation (when the outcome set is smooth).
If trade is permitted, and there are no transaction costs, all outcomes are pareto optimal. That’s what I was objecting to.
I think you might be worried more about maximizing expected (or average) utility than pareto optimization. The two are largely unrelated.
Again, I may be misunderstanding something, but the requirement that there be a universal scale for utility seems to require that individuals be interchangeable, if the scale is dependent on observable characteristics (e.g. someone who has $200 has 2 utils of happiness). Unless this scale is somehow contingent on measuring subjective utility, you’re saying that pareto optimality should be possible only when players have an agreed-upon set of preferences.
Even if I’m confused on that point, I still fail to see how this hypothetical relates to anything in reality.
If people are Pareto optimal in a trade, then yes, that trade is Pareto optimal.
However if there are three trades between three people (12, 23 and 31) and each trade is Pareto-optimal, that does not mean that the set of three trades as a whole is Pareto-optimal. It’s generally possible to change these trades and get a better outcome for everyone (which is kinda what a market with price signals tries to do).
The only cases where you cannot do this is precisely where there is an agreed upon weighting of everyone’s utility function etc...
The individuals need not be interchangeable, the weighting need not be fair. But Pareto-optimality is only possible in this situation (when the outcome set is smooth).