By Gaertner W.

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**Extra info for A primer in social choice theory, Edition: Rev.Ed.**

**Example text**

Under the new notation, simple majority voting represents a social aggregation rule g that gives D = +1, −1, 0 according as the number of +1’s, denoted as N (1), minus the number of −1’s, denoted as N (−1), is positive, negative, or zero. Let us turn to the sufﬁciency part of the proof. The ﬁrst thing to notice is that since g satisﬁes condition A , the value of g (d1 , . . , dn ) only depends on the number of +1’s, −1’s, and the number of 0’s in the list and not on the positions of the +1’s, −1’s, and 0’s in the list.

Dn ) ≥ 0 implies g (d1 , . . , dn ) = +1. 1. It is easy to see that the simple majority rule fulﬁls all four conditions above. Under the new notation, simple majority voting represents a social aggregation rule g that gives D = +1, −1, 0 according as the number of +1’s, denoted as N (1), minus the number of −1’s, denoted as N (−1), is positive, negative, or zero. Let us turn to the sufﬁciency part of the proof. The ﬁrst thing to notice is that since g satisﬁes condition A , the value of g (d1 , .

A four-ﬁfths majority rule apparently is a bit more responsive than the rule just given but less responsive than a two-thirds majority rule which, again, is less responsive than the absolute majority rule. We use more (respectively less) responsive here in the sense of inducing a change of social preference ‘away from’ the status quo y. More (less) THE SIMPLE MAJORITY RULE 39 responsive then means to induce a change to x, let’s say, with the support of a smaller (larger) fraction of the voters who strictly prefer x to y.