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I suggest you look at the ordered logistic SHAZAM routines prepared by Daehoon Nahm at Macquarie SHAZAM Ordered and Multinomial Logit Procedures. His routine prints out the coefficients (and the prediction success table) and you can calculate the odds ratio afterwards from the output by exponentiating the ordered logit coefficients.

Ordered logit is estimation over the levels of your dependent variable (rank) so the odds ratio is comparing the votes of people who are in groups greater than k versus those who are in groups less than or equal to k, with k being the level of the response variable. The interpretation would be that for a one unit change in the particular predictor variable (e.g. age), the odds for cases in a group that is greater than k versus a group that is less than or equal to k are the (proportional odds) times larger. e.g. if the Odds ratio of a variable e.g. age are say 3.2 then the odds of the the vote being for the the rank > K would be just over 3 times larger.