A real-valued function on S_n is *linear* if it is a linear combination of indicators of the form "i goes to j".

Ellis, Friedgut and Pilpel showed that if a linear function on S_n is Boolean then it is a *dictator*, that is, it depends on the image of some i or on the inverse imageof some j.

What can we say about linear functions on S_n which are *almost* Boolean?

We answer this question completely for several notions of "almost", improving on earlier results together with Ellis and Friedgut. LOCATION:The link will be sent to you after registration END:VEVENT END:VCALENDAR