for ½, when (9.1) 0 0  < <  ≤ for ½, when  or  (9.2) 0 1 ½ < 1 ≤ ≤ ≤ In order to gain a better understanding of what is involved, figure 1 shows the range of values of (upper and lower limit) that yield for parameter values of   > 0 0.1, 02, and and and The pattern that emerges is 0.3, 0.4, 0.6, 0.7, 0.8 0.9, 0.1, 0.3, 0.5 0.9. widely diverse. For the interval of values of (= war effectiveness of that lead  0.1 A) to power-sharing shrinks as (= election effectiveness of rises for values of but  <½, A) it increases as while the opposite is true for and it is nevertheless >½, =0.3 =0.5; widest (0, as the destructive effect of war increases, and ½) =0.9, <½. Finally, equation (8) can also be used to identify when the two rivals will agree to lay down their weapons and adopt majoritarian politics. Setting and solving we obtain k* = 0 = . (9.3) 1– That is, the two rivals will choose to establish a majoritarian democracy in the case where election-war relative effectiveness equals the marginal income surviving the war. A’s Since it is only by chance that this special condition is satisfied in practice, adoption of majoritarian democracy by the mutual agreement is unlikely. Figure 1: Values of which and choose power-sharing given , and A B R Figure 1 continued – 3.3 Conflict and power-sharing under risk aversion
for ½, 0 when 0 ≤  < < (9.1) for ½, 0 when ≤  1 or ½ ≤  <  ≤ 1 (9.2) In order to gain a better understanding of what is involved, figure 1 shows the range of values of  (upper and lower limit) that yield  > 0 for parameter values of 0.1, 02, 0.3, 0.4, 0.6, 0.7, 0.8 and 0.9, and 0.1, 0.3, 0.5 and 0.9. The pattern that emerges is widely diverse. For 0.1 the interval of values of  (= war effectiveness of A) that lead to power-sharing shrinks as (= election effectiveness of A) rises for values of <½, but it increases as >½, while the opposite is true for =0.3 and =0.5; it is nevertheless widest (0, ½) as the destructive effect of war increases, =0.9, and <½. Finally, equation (8) can also be used to identify when the two rivals will agree to lay down their weapons and adopt majoritarian politics. Setting k* = 0 and solving we obtain 1– = . (9.3) That is, the two rivals will choose to establish a majoritarian democracy in the case where A’s election-war relative effectiveness equals the marginal income surviving the war. Since it is only by chance that this special condition is satisfied in practice, adoption of majoritarian democracy by the mutual agreement is unlikely. Figure 1: Values of which A and B choose power-sharing given ,  and R Figure 1 – continued 3.3 Conflict and power-sharing under risk aversion
GT-PEPowerSharing.docx