In a multi-ethnic society, friendship among children might be expected to be overwhelmingly shaped by ethnicity and cultural heritage. Using an original panel data-set of classmate networks in multi-ethnic primary schools near Florence, Italy, (N=396 children in 2nd and 5th grade), we show instead that cognitive skills and personality traits matter as much as ethnicity in shaping friendships, thus playing the role of elective affinities. We test whether friends affect a child’s personality more than the other way round: to do this, we estimate peer effects. We only find non-significant effect of peers on math grades and a measure of intelligence (KBIT). For personality traits, peer effects are significant only for Extraversion. These findings are crucial for design of immigration policies: rather than emphasizing differences among ethnic groups, a farsighted policy could try to point these elective affinities among individuals.