Weight_i is proportional to 1 / sigma_i, normalised so the weights sum to one. It is the simplest allocation rule that treats risk rather than capital as the thing being divided.
Worked on three assets with annualised volatilities of 10%, 20% and 40%: inverse values are 0.10, 0.05 and 0.025, which normalise to 57%, 29% and 14%. The low-volatility asset takes four times the capital of the high-volatility one and each contributes roughly the same volatility to the total.
It ignores correlation and expected return entirely, which is both its weakness and the reason it is robust - there are no estimates to get wrong except volatility, which is the most stable input available. It also tends to load heavily into whatever is currently quiet, so it can concentrate in assets whose calm is about to end.
Related: equal-risk-weighting, risk-contribution, volatility-targeting, percent-volatility-sizing