Scoring rules on dichotomous preferences

In this paper, we study individual incentives to report preferences truthfully for the special case when individuals have dichotomous preferences on the set of alternatives and preferences are aggregated in form of scoring rules. In particular, we show that (a) the Borda Count coincides with Approval Voting, (b) the Borda Count is the only strategy-proof scoring rule, and (c) if the size of the electorate is greater than three, then the dichotomous preference domain is the unique maximal rich domain under which the Borda Count is strategy-proof.

[1]  Salvador Barberà,et al.  Voting by Committees , 1991 .

[2]  H. P. Young,et al.  An axiomatization of Borda's rule , 1974 .

[3]  Clemens Puppe,et al.  Non-manipulable domains for the Borda count , 2006 .

[4]  J. H. Smith.  AGGREGATION OF PREFERENCES WITH VARIABLE ELECTORATE , 1973 .

[5]  Michel Regenwetter,et al.  Approval voting and positional voting methods: Inference, relationship, examples , 2004, Soc. Choice Welf..

[6]  Shigehiro Serizawa,et al.  Maximal Domain for Strategy-Proof Rules with One Public Good , 2000, J. Econ. Theory.

[7]  D. Saari,et al.  The problem of indeterminacy in approval, multiple, and truncated voting systems , 1988 .

[8]  David A. Smith.  Manipulability measures of common social choice functions , 1999 .

[9]  P.-C.-F. Daunou,et al.  Mémoire sur les élections au scrutin , 1803 .

[10]  D. Saari.  Susceptibility to manipulation , 1990 .

[11]  Donald G. Saari,et al.  Is approval voting an ‘unmitigated evil’?: A response to Brams, Fishburn, and Merrill , 1987 .

[12]  Roger B. Myerson,et al.  Axiomatic derivation of scoring rules without the ordering assumption , 1993 .

[13]  Shigehiro Serizawa,et al.  A Maximal Domain for the Existence of Strategy-Proof Rules☆ , 1998 .

[14]  Douglas Muzzio,et al.  Approval voting , 1983 .

[15]  Michael Dummett,et al.  The Borda count and agenda manipulation , 1998 .

[16]  Ken-ichi Inada,et al.  A Note on the Simple Majority Decision Rule , 1964 .

[17]  Peter C. Fishburn,et al.  The responsiveness of approval voting: Comments on Saari and Van Newenhizen , 1988 .

[18]  H. Young.  Social Choice Scoring Functions , 1975 .

[19]  Richard Stong,et al.  Collective choice under dichotomous preferences , 2005, J. Econ. Theory.

[20]  Hugo Sonnenschein,et al.  Voting By Quota And Committee , 1988 .

[21]  Jean-Antoine-Nicolas de Caritat Condorcet,et al.  The Political Theory of Condorcet , 1989 .