The outcomes of the 2013 German Bundestag (federal parliament) are analyzed from the viewpoint of direct democracy. For this purpose, the party positions on 36 topical issues are compared with the results of public opinion polls, and the party and coalition indices of popularity (the average...

The outcomes of the 2013 German Bundestag (federal parliament) election are analyzed from the viewpoint of direct democracy. For this purpose, the party positions on 36 topical issues are compared with the results of public opinion polls, and the party and coalition indices of popularity (the...

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, such as approval voting, in which voters can give two grades—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the...

Collective decision making problems can be seen as finding an outcome that is closest to a concept of consensus. 1 introduced Closeness to Unanimity Procedure as a first example to this approach and showed that the Borda rule is the closest to unanimity under swap distance a.k.a the 2 distance....

The well-known swap distance (Kemeny (1959); Kendall (1938); Hamming (1950)) is analyzed. On weak preferences, this function was characterized by Kemeny (1959) with five conditions; metric, betweenness, neutrality, reducibility, and normalization. We show that the same result can be achieved...

The main purpose of this paper is to estimate the probability of casting a decisive vote for a class or random electorate models encompassing the celebrated IC and IAC models. The emphasis is on the impact of correlation across votes on the order of magnitude of this event. Our proof techniques...

Power indices have been used to evaluate the allocation of power in a wide range of voting situations. While they use the language of game theory known measures of a priori voting power are hardly more than statistical expectations assuming the random behaviour of the players. We introduce a...

A decision scheme (Gibbard, 1977) maps profiles of strict preferences over a set of social alternatives to lotteries over the social alternatives. A decision scheme is weakly strategy-proof if it is never possible for a voter to increase expected utility (for some vNM utility function consistent...