Supplementary material 2. – Test of two point predictions

1.  Maxi-min point

Definition of Maxi-min point:

The Maxi-min point maximizes the lowest payoff in the committee. It thus follows Rawl’s (1971, 302) second principle of justice that inequalities should be arranged “to the greatest benefit of the least advantaged”.

Coordinates and payouts in Maxi-min points

Treatment / Coordinates / Payouts
A / B / C / D / E
LIT / (67|63) / 884 / 810 / 722 / 764 / 724
(67|64) / 886 / 808 / 724 / 771 / 722
HIT / (86|74) / 761 / 667 / 609 / 437 / 436
(87|75) / 754 / 659 / 603 / 441 / 436
(88|76) / 746 / 650 / 597 / 444 / 436
(90|77) / 732 / 636 / 584 / 436 / 444
(91|78) / 724 / 627 / 578 / 436 / 441
(92|79) / 716 / 619 / 572 / 436 / 437
MT / (67|63) / 649 / 453 / 264 / 347 / 266
(67|64) / 653 / 446 / 266 / 361 / 264

Analysis of experimental results

As there is no unique Maxi-min point in the treatments, I compute the distance of every committee decision to its nearest Maxi-min point. The following table compares the distance of chosen outcomes to the core and the distance of chosen outcomes to its nearest Maxi-min point.

Distance of committee decisions to core and Maxi-min point

Treatment / Distance to core < Distance to nearest Maxi-min point / Distance to core > Distance to nearest Maxi-min point / Distance to core = Distance to nearest Maxi-min point / Selection of Maxi-min point
LIT / 178 / 42 / 0 / 0
HIT / 183 / 57 / 0 / 0
MT / 188 / 52 / 0 / 1

Only a single committee decision in MT results in the selection of a Maxi-min point. Moreover, most decisions are closer to the core than to a Maxi-min point.

2.  Fair point (Fiorina and Plott 1978, 583)

Definition of Fair point:

Fiorina and Plott (1978, 583):

Fair Point. Pilot experiments suggested that a likely candidate for a "fair" outcome was the average of the points of individual maximum. This point also happens to be the centroid, the point which minimizes the sum of Euclidean distance from the points of individual maximum.

Coordinates of Fair point in all treatments: (58.3|69.4)

Distance of committee decisions to core and Fair point

Treatment / Distance to core < Distance to Fair point / Distance to core > Distance to nearest Fair point / Distance to core = Distance to nearest Fair point / Selection of point within radius of 1.5 units around Fair point
LIT / 162 / 58 / 0 / 0
HIT / 122 / 118 / 0 / 0
MT / 145 / 95 / 0 / 1

Only a single committee decision in MT results in the selection of the Fair point. Moreover, most decisions are closer to the core than to the Fair point. The predictive power of the Fair point is highest in HIT (just below 50%). The Fair point lies to the right of the core and thus coincides with the area of more equally distributed alternatives.

References

Fiorina, M. P., & Plott, C. R. (1978). Committee Decisions under Majority Rule: An Experimental Study. American Political Science Review, 72(2), 575-598.

Rawls, J. (1971). A Theory of Justice. Cambridge: Harvard University Press.