Altruism

Abstract

The French term ‘altruisme’ was introduced by Auguste Comte (1830–42) to signify devotion to the welfare of others, especially as a principle of action. It is closely related to concepts such as benevolence and unselfishness. It has long attracted the interest of moral philosophers (see e.g. Nagel 1970; Milo 1973; Roberts 1973; Collard 1978; Margolis 1982). Rescher (1975, p. 11) categorizes it as one of the ‘modalities’ of unselfishness. Numerous social scientists in many fields, including sociobiology, have been interested in altruistic behaviour as helping to assure species and gene survival (Becker 1976; Collard 1978, ch. 5). While some economists have participated in such research, more have naturally concentrated upon the implications of altruism for economic outcomes–in particular, the allocation of resources and the distribution of income.

The French term ‘altruisme’ was introduced by Auguste Comte (1830–42) to signify devotion to the welfare of others, especially as a principle of action. It is closely related to concepts such as benevolence and unselfishness. It has long attracted the interest of moral philosophers (see e.g. Nagel 1970; Milo 1973; Roberts 1973; Collard 1978; Margolis 1982). Rescher (1975, p. 11) categorizes it as one of the ‘modalities’ of unselfishness. Numerous social scientists in many fields, including sociobiology, have been interested in altruistic behaviour as helping to assure species and gene survival (Becker 1976; Collard 1978, ch. 5). While some economists have participated in such research, more have naturally concentrated upon the implications of altruism for economic outcomes–in particular, the allocation of resources and the distribution of income.

Altruistic Preferences and Utilities

Most of the problems presented by altruism are adequately captured in a simple model with n individuals who each consume a single transferable good – perhaps a Hicks composite commodity, because relative prices are fixed. So an economic allocation is described by an income distribution vector y in ${\boldsymbol{\mathbb{R}}}_{+}^n$ whose typical non-negative component y_i denotes the income of person i. Even intergenerational altruism can be discussed in such a framework, with y_i denoting wealth, provided that capital markets are perfect and no transfers occur which affect real interest rates, and provided that we ignore the special problems that arise when both the time horizon and the number of individuals are infinite.

If individual i has selfish preferences, then income distribution y is preferred to y′ if and only if ${y}_i>{y}_i^{\prime }$ so that i has more income. But altruistic preferences allow y to be preferred to y′ even if ${y}_i<{y}_i^{\prime }$ provided enough other individuals j have gains ${y}_j-{y}_i^{\prime }$ which are large enough to overcompensate. Thus altruistic preferences can be quite a general (complete and transitive) ordering ≳i on ${\boldsymbol{\mathbb{R}}}_{+}^n$.

Some more care is needed here, however. Economists usually identify ‘welfare’ with ‘preferences’ and assume that it can be represented by a welfare function w_i(y) on ${\boldsymbol{\mathbb{R}}}_{+}^n$ which increases as y becomes more preferred. Recalling that altruism is regard for others’ welfare then suggests that i must want to maximize a function of the form ${w}_i={\phi}_i\left({y}_i,{\boldsymbol{w}}_{-i}\right)$ where w_–i denotes the vector of welfare levels w_j (j ≠ i) with i excluded, and where ϕ_i is increasing in every other w_j. Given the income distribution y, finding the individual welfare levels w_i(y) requires solving the n simultaneous equations:

$$ {w}_i=\phi \left({y}_i,{\boldsymbol{w}}_{-i}\right) $$

(1)

for every i. So each w_i(y) is only well-defined provided that these equations have a unique solution. Becker (1974, pp. 1076–7) amongst others discusses this problem – for a special Cobb–Douglas case with two individuals. Assume that Eq. 1 does have a unique solution for every y in ${\boldsymbol{\mathbb{R}}}_{+}^n$, though this is by no means innocuous. In particular, taking the total differential of Eq. 1 gives:

$$ d{w}_i-\sum_{j\ne i}{\phi}_{\mathrm{ij}}d{w}_j={\phi}_{\mathrm{ii}}d{y}_i $$

(2)

and the matrix formed by the coefficients of each dw_j on the left-hand side of each equation in (Eq. 2) must be invertible (see Kolm 1969, pp. 153–4).

Pareto Inefficient Redistribution

When everybody’s altruistic utility function w_i(y) depends upon the incomes of all, it seems obvious that there are externalities likely to cause Pareto inefficiency. Unlike standard externalities, however, individuals can translate their altruism into action by giving income away to anyone they want to. Let t_ij (≥0) denote the transfer made by i to j. Then, assuming that each w_j is differentiable, and recognizing the non-negativity constraints that prevent people taking income from others, transfers occur until the following first order conditions are satisfied for every i, j with i ≠ j:

$$ {w}_{\mathrm{ij}}\le {w}_{\mathrm{ii}},{t}_{\mathrm{ij}}\ge 0\;\mathrm{and}\;{t}_{\mathrm{ij}}\left({w}_{\mathrm{ii}}-{w}_{\mathrm{ij}}\right)=0 $$

(3)

where w_ii denotes ∂w_i/∂y_j. Thus w_ii = w_ij unless the constraint t_ij ≥ 0 binds, when one can have w_ii <w_ij, with i valuing his own income more than j’s at the margin.

First order conditions for Pareto efficiency, on the other hand, require the existence of marginal welfare weights β_ii = (1 to n) such that, for every pair of individuals j, k:

$$ \sum_i{\beta}_i\left({w}_{ij}-{w}_{ik}\right)=0 $$

(4)

so that the marginal social benefit of $1 for j is equal to that of $1 for k. This presumes an interior distribution in which all have income.

Now suppose that Eq. 3 is satisfied at a distribution y^* in which no individual wants to take income from anybody else. Then w_ii = w_ij for all i, j and the efficiency conditions (Eq. 4) are satisfied! But Winter (1969) notices how alleviating poverty can create externalities of the kind that occur when public goods have to be provided by private individuals. After all, a poor person is likely to benefit by receiving income from the rich, even if he is altruistic to the rich. Then w_ij < w_ii, where i is the poor person and j the rich. So Eq. 4 may well be violated. This is especially clear in Arrow (1981), where every individual’s altruistic utility takes the form:

$$ {w}_i\left(\boldsymbol{y}\right)\equiv {u}_i\left({y}_i\right)+\sum_{j\ne 1}\upsilon \left({y}_j\right) $$

(5)

and y_i = y_j implies ${u}_i^{\prime}\left({y}_i\right)>{\upsilon}^{\prime}\left({y}_j\right)$. Arrow shows that, excluding trivial equilibria in which no voluntary redistribution at all takes place, redistribution is only Pareto efficient in a very special case when there is just one rich giver – e.g. the two person case by Hochman and Rodgers (1969). Obviously giving is then not a public good. But as soon as there are two or more givers, Pareto inefficiency is inevitable in Arrow’s model at least (see also Bergstrom 1970; Nakayama 1980).

Policy Relevance

If altruistic preferences make transfers to the poor a public good, this is a prima facie argument for public intervention to redistribute income. Yet this argument has been contested. It has even been claimed that redistributive policy is powerless because it merely substitutes for private charity. In Barro (1974), the issue is obscured by dynamic considerations and the fact that ‘charity’ takes the form of bequests to one’s heirs. Public debt becomes irrelevant because its effects are totally offset by bequests. This presumes, however, that nobody wishes to make negative bequests, because otherwise the national debt is a way of reproducing the effects of negative bequests. Were Barro’s arguments correct, Bernheim and Bagwell (1985) show that then many other policy instruments would also become ineffective; even distortionary income taxes could be offset by reducing bequests in order to pay them. Just as Barro’s neutrality proposition fails when agents could gain from making negative bequests if they were allowed, so redistributive policies are effective precisely when the poor can gain by further transfers from the rich which the rich are unwilling to make because of the public good problem. This is true even when the poor feel altruistic toward the rich.

There are some special cases where neutrality does hold and policy is irrelevant. One is with just one giver, which is the Arrow (1981) sufficient condition for efficiency. Another is Becker’s (1974, p. 1080, 1981) household with a head who is wealthy enough to want to control the intrafamily distribution of income. Then the ‘rotten kid’ theorem has the activities of selfish children completely offset by transfers from the head, provided that the household head is able to retain control even if he should die first (Hirshleifer 1977). Becker never considers, however, a family with two heads, for which the rotten kid theorem would fail in general, with each head providing too little support for efficiency. Warr (1982, 1983) also argues that policy is irrelevant, but analyses only first order conditions like Eq. 3 without any inequalities, and so fails to consider the likely case in which charity is insufficient to make the poor want no more transfers from the rich. Bergstrom and Varian (1985) and Bergstrom et al. (1986) provide further discussion.

Is Charity Public Good?

The flawed policy irrelevance argument is not the only way to contest treating redistribution as a public good when there is altruism. A better argument is due to Sugden (1982, 1983, 1985) who questions whether individuals’ altruistic behaviour maximizes a utility function which can be expressed solely as a function of the income distribution. Suppose that A likes to give 10% of his marginal income to charity C. Suppose too that B gives $10 less to charity C than before. Then this is like a $10 fall in A’s total income, leading to a $1 drop in the amount A wants C to receive in total, so A increases his giving to C by $9 in order to bring this about. Conversely, if B gives $10 more to charity C, then A will reduce his giving by $9. This is a general feature of privately provided public goods: the more one person gives, the less others will want to. In the case of charity, however, such negative covariation between different people’s giving seems implausible. It would imply (Sugden 1983) that the main beneficiaries of a new gift to a charity are those other givers who respond by reducing their gifts to that charity! Sugden concludes that givers value charity per se as well as for the help it gives the recipients-a possibility discussed earlier by Arrow (1974), amongst others. Then each person’s giving becomes a separate private good, and the public good argument for replacing charity by tax-financed transfer programmes becomes less convincing.

Charity: Real or Apparent Altruism?

An obvious explanation of behaviour such as charitable giving is altruistic preferences. Yet it is not the only possible explanation. As just discussed, gifts may be made for their own sake as well as because of an altruistic regard for the recipient’s welfare. They may also reflect egoistic cooperative behaviour, however, as discussed by Boulding (1973), Arrow (1974), and Hammond (1975), amongst economists, and by many sociobiologists – as has been pointed out by Becker (1976), Kurz (1977, 1978), etc. If persons A and B are in continual contact, both may gain from reciprocal cooperation as a form of mutual insurance. And if there is an infinite chain A₁, A_2,A_3,… with person A_n in contact with A_n+1, all can gain from maintaining cooperation into the indefinite future. Genes which promote such cooperation enhance their prospects of long-run survival. Maintaining such cooperation requires deviants to be punished suitably. But apparently altruistic behaviour emerges from entirely selfish preferences. The same is true when it is clear to all members of a group that one of their members must act for their mutual benefit, although there may be a costly or dangerous delay before the apparently altruistic behaviour emerges, as in Bliss and Nalebuff’s (1984) model of brinkmanship. Finally, Sugden’s (1984) theory of reciprocity is an interesting recent explanation of apparently altruistic behaviour which is really selfish at bottom.

Is Altruism Relevant?

It has just been seen that altruistic preferences may be unnecessary to explain apparently altruistic behaviour. This limits the relevance of altruism for positive economics, though one cannot deny that some behaviour is indeed motivated by altruism in the sense of devotion to the welfare of others.

A more controversial claim is that altruism also has limited relevance for normative economics. This issue is addressed by Barry (1965, p. 65) because altruistic regard for others is an instance of a ‘publicly oriented want’, which ‘carries a claim to satisfaction only as being a want for what ought to be done anyway’, thus people’s altruistic preferences are irrelevant in determining what should be the distribution of income, except in so far as they correspond to what is anyway ethically appropriate. In the language of welfare economics, each individual’s welfare corresponds only to that person’s ‘privately-oriented’ or selfish preferences. Altruism is therefore excluded, because it is regard for others’ welfare. That is not to deny that welfare-relevant externalities may arise if, for instance, a rich person experiences revulsion on being confronted with extreme poverty. But avoiding such revulsion is not altruism so much as selfish behaviour.

A related reason for excluding altruistic preferences from welfare is to avoid undesirable double counting. Suppose that A is an altruist with utility $u\left({y}^A\right)+\left(1/2\right)u\left({y}^E\right)$ for the distribution of income between A and E, an egoist. Suppose that E, however, has a selfish utility function u(y^E). Adding utilities then gives $u\left({y}^A\right)+\left(3/2\right)u\left({y}^E\right)$, with greater weight for the marginal utility of the undeserving egoist’s income than for the deserving altruist’s. A more appropriate welfare function is $u\left({y}^A\right)+u\left({y}^E\right)$ which disregards A’s altruism and just adds selfish utilities. The main role of altruism in welfare economics is to help determine ethical views, not to determine individual welfare. Concepts of Pareto efficiency which include altruism in individual welfare have little normative significance, as do the alleged ‘Pareto efficient’ income redistributions. Altruistic behaviour often helps to promote social welfare, but it may not if the altruism happens to be directed toward those whose income should receive only small weight in the social welfare function.

See Also

• Envy

• Equity

• Externalities

• Family

• Gifts

• Public Goods

• Wicksteed, Philip Henry (1844–1927)