Fiscally Stable Income Distributions under Majority Voting and Bargaining Sets

We explore two variants of the Bargaining Set in a simple majority gameon income distributions in order to understand the apparent stability of taxschedules in democratic societies, despite the fact that the core of such gamesis empty (no majority Condorcet winner). Those variants are sharper thanin the literature (Mas-Colell (1989), Shitovitz (1989), Zhou (1994)), by requiringthat counterobjections try to garantee their initial income levels toall members of the minority who stand to lose in an objection. A first variantdefines as usual an income disbribution to be stable if there is no objectionagainst it that is "justified", i.e. for which there is no counterobjection satisfyingthe above requirement. A second variant alllows objecting majoritiesto look one more step ahead. An objection is "weakly justified" if, wheneverthere is a counterobjection, the objecting majority can beat it while guaranteeingtheir income levels to all of its members. An income distribution isstongly stable if there is no weakly justified objection against it.These two variants generate sharper solution sets than when applied tolarge market games as in Mas-Colell (1989), Shitovitz(1989). An incomedistribution is stable if and only if its Lorenz curve has no point in commonwith the graph C of f : [1=2; 1] ! [0; 1], with f (b) = 1¡1= (2b) ; for b > 1=2:It is strongly stable if and only if it is the egalitarian one.