  We revisit Machina's local utility as a tool to analyze attitudes to
multivariate risks. We show that for non-expected utility maximizers choosing
between multivariate prospects, aversion to multivariate mean preserving
increases in risk is equivalent to the concavity of the local utility
functions, thereby generalizing Machina's result in Machina (1982). To analyze
comparative risk attitudes within the multivariate extension of rank dependent
expected utility of Galichon and Henry (2011), we extend Quiggin's monotone
mean and utility preserving increases in risk and show that the useful
characterization given in Landsberger and Meilijson (1994) still holds in the
multivariate case.
