Turning relative deprivation into a performance incentive device

ABSTRACT

The inclination of individuals to improve their performance when it lags behind that of others with whom they naturally compare themselves can be harnessed to optimize the individuals’ effort in work and study. In a given set of individuals, we characterize each individual by his relative deprivation, which measures by how much the individual trails behind other individuals in the set doing better than him. We seek to divide the set into an exogenously predetermined number of groups (subsets) in order to maximize aggregate relative deprivation, so as to ensure that the incentive for the individuals to work or study harder because of unfavorable comparison with others is at its strongest. We find that the solution to this problem depends only on the individuals’ ordinally measured levels of performance independent of the performance of comparators.

KEYWORDS:

• Social preferences
• Relative deprivation
• Effort elicitation
• Assignment to groups
• Performance optimization

Notes

¹ This argument is broadly in line with Akerlof (1997).

² Here and henceforth, if $r=0$, then $\{1,2,\dots ,r\}=\text{empty}$.

³ Quite obviously, the maximal value of $ARD(\{X_1,X_2\})$ depends on $(a_1,a_2,\dots ,a_n)$. As calculated in Example 1, for $N=4$ and $(a_1,a_2,a_3,a_4)=(1,2,3,4)$, the maximal value of $ARD(\{X_1,X_2\})$ is $2$. For $N=4$ and $(a_1,a_2,a_3,a_4)=(1,2,4,10)$, the maximal value of $ARD(A,B)$ is $5.5$. Nonetheless, in both cases, the set of optimal divisions $\{\{\{4,1\},\{3,2\}\},\{\{4,2\},\{3,1\}\}\}$ is the same.

⁴ By a permutation of the sets $Z_1,Z_2,\dots ,Z_m$ we mean here a sequence of permutations $({\sigma }_1,{\sigma }_2,\dots ,{\sigma }_m)$ such that ${\sigma }_i$ is a permutation of $Z_i$ for $i=1,2,\dots ,m$.

⁵ The reference (comparison) group of an individual is the set of individuals with whom the individual naturally compares himself. (Consult Runciman, 1966; Singer, 1981.)

⁶ The empirical findings support the relative income hypothesis. Duesenberry (1949) already found that individuals’ levels of savings depend on their positions in the income distribution, and that the incomes of the richer people affect the behavior of the poorer ones (but not vice versa). Later on, and for example, Schor (1998) showed that, keeping annual and permanent income constant, individuals whose incomes are lower than the incomes of others in their community save significantly less than those in their community who are relatively better off.