I have no idea [what my IQ is]. People who boast about their IQ are losers – Stephen Hawking
A quick and dirty signalling explanation as to why Hawking is right:
If we accept that IQ is a fairly good measure of how good you’ll be at your job, how intelligent you are, and things like that, having a high IQ is something worth bragging about, as you can use it to tell others how clever you are.[ref]There are a number of ways of doing this besides going “my IQ is X” – high-IQ societies might be a slightly more subtle (and superior) way of signalling: “My IQ is (at least) X”.[/ref]
However, this signalling has a sell-by date. IQ is only a proxy measure or predictor of intellectual achievement, and not achievement itself – no one has made the world a better place by acing a standardized test. When one is young, one might only have proxy measures to go on: we would expect the child with an IQ of 150 to have a better chance of winning a Nobel prize than one with an IQ of 90. Once one is an adult we can stop looking at the proxy measures and instead look at whatever record of achievement there is.
If Stephen Hawking wanted to brag about how clever he is, his IQ (however high it may be) would come a long way down the list of braggables like “I held the Lucasian chair in mathematics at Cambridge” or “I discovered Hawking radiation”. If his IQ was much lower than we would expect him to have, sensible people wouldn’t go: “Oh that Hawking only has an IQ of 102, he’s not that bright after all”, but more likely to go “His intelligence must be one of the exceptions that isn’t captured by IQ tests”, or something like that.
In contrast, it might still be worth bragging about your IQ if you haven’t achieved much (or at least much less than your IQ score would lead us to expect). If you are a loser by conventional measures of intellectual achievement, then telling us you have a really high IQ may encourage us to think you’re really clever but underachieving, or that you have (or had!) lots of potential, which is a bit better than us thinking you are a garden-variety loser.
If so, we should expect people to be more likely to boast about their IQ the more their IQ overpredicts their actual achievements (which, seems about right from my own experience). So people who boast about their IQ are (generally) losers.