You’re absolutely right in my opinion Abraham. EV is a mathematical convenience and simplification that might work most of the time, but certainly not all.
I feel words like “expected value” are confusing & miselading (nothing expected about it—it’s a misnomer and accident of history/ translation from french that it’s called that), and this community would do well to avoid unnecessary jargon. I need to write up a post about this.
If we substituted the word “expected value” with mean or average, which is literally what it is (and I meet so many people in this community who get this wrong), it would be just as accurate but much more easier to understand, even to technical people. And many people understand that mean is not always the most appropriate statistic to use espescially with skewed distributions, e.g. reporting on incomes is often done with median, and that’s perfectly fine.
Expected value should also not be confused with expected utility (or as I prefer the mean utility). You use the terms interchangeably in your post as do many people in this community, it’s fine in causal conversation but it is worth being specific when necessary in discussions like this. I suspect because the word “value” in expected value implies some humanistic desireable ideal, but that’s what the word utility is for.
You also say use the term “in expectation” to mean the most likeliest outcome (i.e. the mode outcome) or more than 50%. I’m not familiar with that langauge—maybe it is accurate, but to me it is confusing when you can simply say the mode or the likeliest outcome.
So ultimately I suspect your dilemmas boil down to the recognition that there are circumstances where mean, mode, median, (and in fact even more statistics) can be maximised and we get different optimal decisions depending on the statistic we use.
At the end of the day we want to: maximise utility. But if utility has a probability distribution, it’s hard to maxmise without using some statistic (mean, mode, median etc) that maps a probability distribution to a real number. Using mean (EV) is not completely arbitrary I believe (it has some nice preperties), but it’s not fully settled. I personally think it has problems.
You’re absolutely right in my opinion Abraham. EV is a mathematical convenience and simplification that might work most of the time, but certainly not all.
I feel words like “expected value” are confusing & miselading (nothing expected about it—it’s a misnomer and accident of history/ translation from french that it’s called that), and this community would do well to avoid unnecessary jargon. I need to write up a post about this.
If we substituted the word “expected value” with mean or average, which is literally what it is (and I meet so many people in this community who get this wrong), it would be just as accurate but much more easier to understand, even to technical people. And many people understand that mean is not always the most appropriate statistic to use espescially with skewed distributions, e.g. reporting on incomes is often done with median, and that’s perfectly fine.
Expected value should also not be confused with expected utility (or as I prefer the mean utility). You use the terms interchangeably in your post as do many people in this community, it’s fine in causal conversation but it is worth being specific when necessary in discussions like this. I suspect because the word “value” in expected value implies some humanistic desireable ideal, but that’s what the word utility is for.
You also say use the term “in expectation” to mean the most likeliest outcome (i.e. the mode outcome) or more than 50%. I’m not familiar with that langauge—maybe it is accurate, but to me it is confusing when you can simply say the mode or the likeliest outcome.
So ultimately I suspect your dilemmas boil down to the recognition that there are circumstances where mean, mode, median, (and in fact even more statistics) can be maximised and we get different optimal decisions depending on the statistic we use.
At the end of the day we want to: maximise utility. But if utility has a probability distribution, it’s hard to maxmise without using some statistic (mean, mode, median etc) that maps a probability distribution to a real number. Using mean (EV) is not completely arbitrary I believe (it has some nice preperties), but it’s not fully settled. I personally think it has problems.