The paradox of grading systems

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.     

Multiwinner approval voting: an apportionment approach

Public Choice - To ameliorate ideological or partisan cleavages in councils and legislatures, we propose modifications of approval voting in order to elect multiple winners, who may be either...     

Condorcet Polling

For a single-winner multi-candidate election, it is broadly accepted that the Condorcet candidate (if one exists) should win. Voting systems do not always elect the Condorcet winner. Public opinion polls are not generally designed to try to identify a Condorcet candidate. They could easily be constructed to do so, however. The resulting process may be called Condorcet polling, for which various designs are presented herein. Information from Condorcet polling may enable some voters, under a plurality or runoff system, to bring about an outcome they prefer by voting strategically for the Condorcet candidate when they would not otherwise do so.     

Scheduling of panels by integer programming: Results for the 2005 and 2006 New Orleans meetings

This note reports on the successful use of an integer-programming routine, whose details were delineated earlier, to assign panels to time slots in scheduling the annual meetings of the Public Choice Society in New Orleans in both 2005 and 2006. Each panel, or session, consists of three or four papers and belongs to a specific subject area. All submitted papers are grouped into panels in an initial step. The integer-programming routine then assigns these panels to the available time slots so as to satisfy certain constraints and, in addition, spread the panels in each subject area as evenly as possible across the time slots. Problems that arose, and possible solutions, are briefly discussed.     

Use of Integer Programming to Optimize the Scheduling of Panels at Annual Meetings of the Public Choice Society

Preparation for the annual meetings of an organization such asthe Public Choice Society involves scheduling various panels(sessions) in the available time slots. No person can bescheduled for more than one panel in the same time slot. Eachpanel belongs to a specific subject area; one tries to spreadthe panels in each area among the time slots as evenly aspossible. We develop an integer-programming model to produce aschedule that maximizes the evenness subject to theconstraints. We successfully applied the modelretrospectively, as a test case, to schedule the 2001 annualmeetings of the society.