Apply social policy 1 (suitably scaled down) to beakers S1 and M1, and social policy 2 to S2 and M2. The question of social choice becomes choosing one set of beakers in preference to another.
We will use ordinal methods whenever possible due to the difficulty of agreeing on numbers for different people's utilities.
Rawls (Maximin): touch and compare
all four beakers to identify the coldest one.
If the coldest beaker is S1 or M1, choose policy 2
if the coldest beaker is S2 or M2, choose policy 1.
Harsanyi: Mix together beakers S1
and M1 in one bucket.
Mix together beakers S2 and M2 in another bucket.
Touch and compare the two mixtures; choose the policy whose mixture is warmer.
Pareto: Touch
and compare M1 and M2. Touch and compare S1 and S2.
If S1 is warmer than S2 and M1 is warmer than M2, choose policy 1.
If S2 is warmer than S1 and M1 is warmer than M1, choose policy 2.
If M1 and M2 are equally warm, choose the policy for which Sam's beaker is
warmest.
If S1 and S2 are equally warm, choose the policy for which Mary's beaker is
warmest.
BUT, if S1 is warmer than S2 and M2 is warmer than S1, or vice versa, make
no decision!
Nash: Use a thermometer to measure
the temperature of the two reservoirs; call these temperatures s0 and m0.
Also measure the temperatures of the four beakers: ml, m2, s1, and s2.
| If |
(m1-m0) |
> | (s2-s0) |
pick policy 1, otherwise
pick policy 2. |
| (m2-s0) |
(sl-s0 |
(Note Nash is the only one that requires a thermometer. The ratios are the same whether it is Celsius or Fahrenheit.))