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You're technically correct--the distribution carries a lot more information than the average or median alone. The problem is that many of these decisions are b

You're technically correct--the distribution carries a lot more information than the average or median alone. The problem is that many of these decisions are being made democratically, or by democratically elected representatives. They need to be able to explain the impact of their decisions to the average voter. Having a single number that goes up or down makes communication and coordination a lot easier, and I think it's worth discussing what the best single number might be.

coldtea 4y ago
Or those "elected represenatives" could help educate the people - to e.g. understand distributions. But instead they educate them in BS, both in schools, and through their government communication. It's more convenient to emphasize BS in curriculums than proper life/political skills...
scarmig 4y ago
Choosing a single number necessarily removes information about the distribution, though, and which information is being discarded is inherently a political decision. The Rawlsian veil of ignorance (at least a naive version) would have us choose p0 as the meaningful number; a utilitarian with certain beliefs about the marginal utility of money would prefer the distribution mean. Even the choice to use a normalize GDP per capita is taking a strong stance on the repugnant conclusion.
JackFr 4y ago
> They need to be able to explain the impact of their decisions to the average voter. No, not the “average” voter - messaging should be aimed at the marginal voter.
- quickthrower2 4y ago
  Well a distribution across all voters. Some voters are more swing-able than others. Some voters are in more marginal seats than others. But all voters can swing given enough "force". If the force is negative force for who they normally vote for.
- taneq 4y ago
  Exactly, after all they’re not trying to actually implement (or even determine!) the will of the people, they’re just trying to stay in power.
taneq 4y ago
> Having a single number that goes up or down makes communication and coordination a lot easier And this is why demagogues win. It’s much easier to seem competent by confidently shouting simple platitudes than by attempting a nuanced discussion.
- superb-owl 4y ago
  I think there's a middle ground between having a simple, understandable message and just spouting nonsense. Granted we have a lot more of the latter these days.
ramraj07 4y ago
If I really have to go with a single number I’d go with a trimmed mean, this comes after a long stint both in academia and trying to generate metrics pipelines in industry.
- superb-owl 4y ago
  Correct me if I'm wrong, but I think Trimmed Mean does well with normal distributions with some outliers. Weath doesn't follow a normal distribution even approximately, so variations on the mean will often give counterintuitive results.
  - ramraj07 4y ago
    I’ve used it in many contexts and compared mean median and trimmean in many different distributions (even bimodal ones); trimmed mean works amazingly well and is very robust at representing the data’s central tendency in many contexts. Depending on how much you trim it, it can essentially get close to a mean or a median anyway. So consider it more as a mean or median but with a bit less outliers or a bit more extra context respectively.
rightbyte 4y ago
Politicians allready talk about e.g. poor people, workers, middle class and rich. So I don't think a concrete group division is too hard for them. Percentiles might be too much to ask though ...

coldtea 4y ago

Or those "elected represenatives" could help educate the people - to e.g. understand distributions. But instead they educate them in BS, both in schools, and through their government communication. It's more convenient to emphasize BS in curriculums than proper life/political skills...

scarmig 4y ago

Choosing a single number necessarily removes information about the distribution, though, and which information is being discarded is inherently a political decision. The Rawlsian veil of ignorance (at least a naive version) would have us choose p0 as the meaningful number; a utilitarian with certain beliefs about the marginal utility of money would prefer the distribution mean. Even the choice to use a normalize GDP per capita is taking a strong stance on the repugnant conclusion.

JackFr 4y ago

> They need to be able to explain the impact of their decisions to the average voter. No, not the “average” voter - messaging should be aimed at the marginal voter.

quickthrower2 4y ago
Well a distribution across all voters. Some voters are more swing-able than others. Some voters are in more marginal seats than others. But all voters can swing given enough "force". If the force is negative force for who they normally vote for.
taneq 4y ago
Exactly, after all they’re not trying to actually implement (or even determine!) the will of the people, they’re just trying to stay in power.

taneq 4y ago

> Having a single number that goes up or down makes communication and coordination a lot easier And this is why demagogues win. It’s much easier to seem competent by confidently shouting simple platitudes than by attempting a nuanced discussion.

superb-owl 4y ago
I think there's a middle ground between having a simple, understandable message and just spouting nonsense. Granted we have a lot more of the latter these days.

ramraj07 4y ago

If I really have to go with a single number I’d go with a trimmed mean, this comes after a long stint both in academia and trying to generate metrics pipelines in industry.

superb-owl 4y ago
Correct me if I'm wrong, but I think Trimmed Mean does well with normal distributions with some outliers. Weath doesn't follow a normal distribution even approximately, so variations on the mean will often give counterintuitive results.
- ramraj07 4y ago
  I’ve used it in many contexts and compared mean median and trimmean in many different distributions (even bimodal ones); trimmed mean works amazingly well and is very robust at representing the data’s central tendency in many contexts. Depending on how much you trim it, it can essentially get close to a mean or a median anyway. So consider it more as a mean or median but with a bit less outliers or a bit more extra context respectively.

rightbyte 4y ago

Politicians allready talk about e.g. poor people, workers, middle class and rich. So I don't think a concrete group division is too hard for them. Percentiles might be too much to ask though ...