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many people mistakenly assume that the concept of utility is a meaningless tautology. they believe it's both the thing we're trying to optimize and the thing we're trying to measure. however, this is a fundamental misunderstanding. utility can be expressed as a significant mathematical concept with practical applications.

let's imagine a scenario where you have a set of options, and we're going to create two lotteries. one lottery might have a 20% chance of outcome x, a 50% chance of outcome y, and a 30% chance of outcome z. another lottery could offer a 100% chance of outcome x. now, let's say you want to provide a heuristic so that an agent acting on your behalf can consistently pick the more preferable lottery.

the concept of utility comes into play here as a practical solution. the most efficient way to compress that heuristic is to assign a scalar "utility" value to each option. the agent can then choose the lottery with the highest expected utility by calculating the sum of each probability multiplied by its corresponding utility value.

in summary, utility is far from a meaningless tautology. it is a valuable mathematical concept that can help guide decision-making processes in a variety of situations.