The idea introduced to Arizona is one of the sillier ideas of the year. It is likely that adding an extrinsic reward (the hope of a lottery prize) to the vote will reduce the voters concentration on the election issues. It may get the voter to the poll -- and in Arizona there is a disincentive to vote as juries are drawn from the election rolls rather than from residency rolls -- but the voter's only goal will be to vote rather than to vote sensibly.
If you are interested there is an unpublished op-ed here http://home.comcast.net/~evansmgmtutor/wsb/lettersandopeds/arizona.html.08.07.2006.html
and a discussion of the issue by Professors of Organizational Behavior here:
New York Times Magazine version[Please scroll down]