1. Is the definition of fairness subject to rational choice? Niall Flynn

2. i) Motivation ii) Outline of experiment iii) Inequity averse utility function and test of self-serving point of equity iv) Results

3. Motivation Interdependent preferences: i)Non-experimental literature → -ve effects, e.g. Duesenberry (1949), Frank (1985), Rayo and Becker (2007). ii) Experimental literature → +ve and -ve effects, e.g. Inequity Aversion

4. Motivation Interdependent preferences: i)Non-experimental literature → -ve effects, e.g. Duesenberry (1949), Frank (1985), Rayo and Becker (2007). ii) Experimental literature → +ve and -ve effects, e.g. Inequity Aversion In practice: inequity = inequality: “For most economic experiments it seems natural to assume that an equitable allocation is an equal monetary payoff for all players. Thus inequity aversion reduces to inequality aversion” : Fehr and Schmidt (2005).

5. Motivation Interdependent preferences: i)Non-experimental literature → -ve effects, e.g. Duesenberry (1949), Frank (1985), Rayo and Becker (2007). ii) Experimental literature → +ve and -ve effects, e.g. Inequity Aversion In practice: inequity = inequality: “For most economic experiments it seems natural to assume that an equitable allocation is an equal monetary payoff for all players. Thus inequity aversion reduces to inequality aversion” : Fehr and Schmidt (2005). Inequity Aversion: If individual is above/below point of equity the payoffs of those below/above point of equity have +ve/-ve effect. Choice of self-serving definition → lowers potential to be above the “fair” allocation → lowers potential for positive externalities and increases potential for negative externalities.

6. Outline of experiment Stage 1: Subjects undertake a 20 minute test of the same 7 “spot-the-difference” questions. Each additional correct answer increases size of endowment used in dictator game. Test is scored via increasing returns to performance production function in order to create different possible definitions of fairness. Y= y i + y j = f(q i ) + f(q j );i,j = 1,2,i  j ;f(q i )>0, f  (q i )>0 Where:Y = dictator game endowment q i = number of questions answered correctly by player i y i = f(q i ) = income generated by player i Scoring system as follows: 1 question correct: generates £0.50 2 question correct: generates £1.00 3 question correct: generates £2.00 4 question correct: generates £4.00 5 question correct: generates £8.00 6 question correct: generates £16.00 7 question correct: generates £32.00

7. Outline of experiment Stage 2: Each subject receives results from stage 1, then one player from each pair is randomly chosen to allocate their endowment. Results are presented to subjects in the following way: By You By Your Partner Total Number of questions answered correctly 6713 Proportion of questions answered correctly 46%54%100% Money generated £16£32£48 Proportion of money generated 33%67%100% Allocation decisions are made in percentiles.

8. Outline of experiment Possible to split subjects into 3 sets: q d >q r, then d is high productivity (H) q d <q r, then d is low productivity (L) q d =q r, then d is equal productivity (E) Three obvious conceptions of fairness: 1.Equal split – i.e. ½ 2.Output ratio – i.e. y i /Y 3.Input ratio – i.e. q i /Q Increasing returns to performance production function means: H: y d /Y > q d /Q > ½ L: ½ > q d /Q > y d /Y E: ½ = q d /Q = y d /Y

9. Outline of experiment Creating pairs: Pairs of subjects are chosen after stage 1 so as to achieve: i)For every dictator in set H there is a unique dictator in set L making an allocation decision for the same endowment – i.e. the same question pairing. ii)Set E contains dictators uniquely matched to those in H and L, but playing for higher endowments. Inducing inequity aversion: No show up fee. Non-neutral language of instructions. Dictator decision made in same room as recipient → very limited anonymity.

10. Inequity-averse utility function x i = income – i.e. absolute amount kept in dictator game Y i = endowment – i.e. amount dictator game is played for Φ i = proportional point of equity – 0 ≤ Φ i ≥ 1 f(x i )>0 g x (.)>0, for x i /Y i > Φ i g xx (.)>0, for x i /Y i > Φ i h(Y i )>0, for Y i >0 h(Y i ) ≤ 0 (1)

11. Inequity-averse utility function xixi Φ i.Y i Y i =Y 1 Y i =Y 2 Where: Y 1 < Y 2 (1)

12. Test of self-serving point of equity (2) For a given endowment and point of equity, and assuming f(.) is linear such that f(x i ) = a + bx i, the FOC of (1) gives an optimal proportional self allocation of:

13. Test of self-serving point of equity Summing (2) within each set and averaging, and assuming that Φ i = ½ for all i in E, gives a lower bound estimates for the average point of equity in set H of: (2) (3) For a given endowment and point of equity, and assuming f(.) is linear such that f(x i ) = a + bx i, the FOC of (1) gives an optimal proportional self allocation of: Average point of equity in Set H Average proportion kept in Set H Average deviation in set E

14. Test of self-serving point of equity Summing (2) within each set and averaging, and assuming that Φ i = ½ for all i in E, gives a lower bound estimates for the average point of equity in set H of: As sets L and H are perfectly matched their points of equity should sum to one if there is no self serving bias, which gives: (2) (3) (4) For a given endowment and point of equity, and assuming f(.) is linear such that f(x i ) = a + bx i, the FOC of (1) gives an optimal proportional self allocation of: Average point of equity Average proportion kept Average deviation in set E

15. Results HLE Matched Set No. Q (d,r)Yx/YQ (d,r)Yx/YQ (d,r)Yx/Y 1 7,6 480.90 6,7 481.00 7,7 641.00 2 7,6 480.75 6,7 480.80 7,7 640.95 3 7,6 480.73 6,7 480.80 7,7 640.8 4 7,6 480.67 6,7 480.50 7,7 640.65 5 7,6 480.67 6,7 480.50 7,7 640.50 6 7,6 480.67 6,7 480.50 7,7 640.50 7 7,6 480.67 6,7 480.44 7,7 640.50 8 6,5 241.00 5,6 240.45 6,6 321.00 9 5,4 121.00 4,5 121.00 5,5 160.75 10 5,4 121.00 4,5 120.90 5,5 160.65 11 5,4 120.67 4,5 120.75 5,5 160.50 12 5,4 120.67 4,5 120.50 5,5 160.50 13 5,4 120.67 4,5 120.50 5,5 160.50 14 5,4 120.67 4,5 120.50 5,5 160.50 15 5,4 120.67 4,5 120.33 5,5 160.50 16 4,3 61.00 3,4 60.5 4,4 80.80 Mean 628.130.775528.130.623637.500.662 SD 0.1460.2150.194

16. E Dictators Allocation to Self E: ½ = q d /Q = y d /Y

17. E Dictators Allocation to Self E: ½ = q d /Q = y d /Y L Dictators Allocation to Self L: ½ > q d /Q > y d /Y

18. E Dictators Allocation to Self E: ½ = q d /Q = y d /Y L Dictators Allocation to Self L: ½ > q d /Q > y d /Y H Dictators Allocation to Self H: y d /Y > q d /Q > ½

19. Results Removing the four highest allocations from each of the three sets gives a data set of solely interior solutions, which can be interpreted as tangency points. This process leaves comparable data sets of: n E =13; n L =10; n H =12 The test derived for self-serving points of equity is tested against a null of: t = 1.17; p=0.121

20. Results Assume utility function of: Which gives an optimal allocation of: Which gives a regression equation of: Where:δ L = dummy variable equal to one if dictator in set L, 0 otherwise δ H = dummy variable equal to one if dictator in set H, 0 otherwise g = gender, f=0; m=1

21. Results Dependent Variable: x i /Y i – i.e. proportional allocation to self 1234 Constant (β 0 ) 0.5255 (0.000) 0.5426 (0.000) Constrained to equal ½ Low Prod Dummy (β 1 ) -0.0356 (0.440) -0.0371 (0.416) -0.0251 (0.534) -0.0139 (0.720) High Prod Dummy (β 2 ) 0.1282*** (0.006) 0.1291*** (0.005) 0.1369*** (0.001) 0.1503*** (0.000) Endowment 0.0010 (0.285) 0.0009 (0.332) 0.0013** (0.045) 0.0015** (0.019) Gender 0.0234 (0.539) -0.0334 (0.295) N 35 R2R2 0.35540.34710.62100.6072 P values in brackets 2. H 0 : (β 0 + β 1 )+(β 0 + β 2 )= 1 ; H 1 : (β 0 + β 1 )+(β 0 + β 2 ) > 1 F(1,30) = 2.48;p=0.063 4. H 0 : β 1 + β 2 = 0 ;H 1 : β 1 + β 2 > 0 F(1,31) = 3.02;p=0.046