1. What is the reason to write (h, yes) and (h, no)? I know that yes and no are options but am not sure what is the principle in writing this way.

2. What is the terminal history talking about in plain words?

Denition 5.2: Binary agenda Let (N, X, b) be an odd-strict collective choice problem with N = {1, . . . , :1}. Let H be a set of sequences containing the empty sequence in which ev- ery element is either Yes or No and for every I E H either - E H and (h,No) E H, in which case I\"; is nonterminal, or there is no value of x for which (h,x] E H, in which case h is terminal. Denote the terminal mem- bers of H byZ and let 0 be a function that assigns to each h E Z an alter- native C(11) e X. Assume that for every x e X we have GUI] = x for some 11 eZ. The binary agenda ((N,X, b),Z, O) is the following extensive game with perfect information and simultaneous moves. Players The set of players is the set N {of individuals). Terminal histories For any prole (v1, . . . , 1;\") with v; G {Yes,No} for all i E N (a vote prole), denote by Terminal histories are sequences of vote proles. Player function For every nonterminal history 11 E H , the player function assigns the set N of all individuals to h. Actions Each player's set of actions after any nonterminal history is {Yes No}. Preferences Each player 1' prefers the terminal history ((1)11, . . ., 1);], . . . , (Hf, . . . , 122]) to the terminal history ((yll, . . . ,y), . . . ,(qu, . . .,y,f)] if and only if O[M(v11,...,v],...,M(uf,..., U)]>g O[M{y11,...,y;),...,M[y1q,...,yf]). Vote (to drop a) Yes No b, c a, b, c Vote (to choose b) Vote (to choose c) Yes No Yes No b C C a, b b C c Vote (to choose a) Yes No a b a b Figure 5.1 An example of a binary agenda