Abstract
Satisficing is a central concept in both individual and social multiagent decision making. In this paper we first extend the notion of satisficing by formally modeling the tradeoff between costs (the need to conserve resources) and decision failure. Second, we extend this notion of “neo”-satisficing into the context of social or multiagent decision making and interaction, and model the social conditioning of preferences in a satisficing framework.
Similar content being viewed by others
Notes
“There are two ways of looking at our duty in the matter of opinion ... We must know the truth, and we must avoid error—these are our first and great commandments as would-be knowers; but they are not two ways of stating an identical commandment, they are two separable laws. ... We may regard the chase for truth as paramount, and the avoidance of error as secondary; or we may, on the other hand, treat the avoidance of error as more imperative, and let truth take its chance” (James 1956, pp. 17,18). Landau and Chisholm (1995) argue that this perspective is also relevant to organizational management: “The difference is not simply semantic, it is that which distinguishes a success-oriented form a failure-avoidance management [emphasis in original].”
Levi’s use of the idea of “probability” here is in the sense of a propensity; that is, the tendency or disposition to yield an outcome of a certain kind.
The importance of interest relative to truth is emphasized by both Whitehead and Popper. “It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occasion of experience is its interest, and is its importance” (Whitehead 1937, PartIV,ChapterXVI). “We must also stress that truth is not the only aim of science. We want more than truth: what we look for is interesting truth [emphasis in original]” (Popper 1963, p. 229).
In the epistemological domain, the probabilistic analogue to this concept is that Prob(B) quantifies the degree to which focusing on B avoids error.
The use of the probability syntax for utilities is not new. Berhold (1973) and Castagnoli and LiCalzi (1996) have interpreted normalized utility functions as probability mass functions, and Abbas and Howard (2005) and Abbas (2009) have applied the probability syntax to utilities for the study of multi-attribute decision problems.
“Complexity is no argument against a theoretical approach if the complexity arises not out of the theory itself but out of the material which any theory ought to handle” (Palmer 1971, p. 184).
References
Abbas, A.E. (2009). From bayes’ nets to utility nets. In: Proceedings of the 29th international workshop on bayesian inference and maximum entropy methods in science and engineering (pp 3–12)
Abbas, A. E., & Howard, R. A. (2005). Attribute dominance utility. Decision Analysis, 2(4), 185–206.
Arrow, K. J. (1986). Rationality of self and others in an economic system. In R. M. Hogarth & M. W. Reder (Eds.), Rational choice. Chicago: University of Chicago Press.
Bacharach, M. (1999). Interactive team reasoning: A contribution to the theory of cooperation. Research in Economics, 23, 117–147.
Bacharach, M. (2006). Beyond individual choice: Teams and frames in game theory. Princeton: Princeton University Press.
Battigalli, P., & Dufwenberg, M. (2009). Dynamic psychological games. Journal of Economic Theory, 144, 1–35.
Bendor, J. B., Kumar, S., & Siegel, D. A. (2009). Satisficing: A ‘pretty good’ heuristic. The B E Journal of Theoretical Economics, 9(1), 1–36.
Berhold, M. H. (1973). The use of distribution functions to represent utility functions. Management Science, 23, 825–829.
Bhatia, S. (2013). Associations and the accumulation of preference. Psychological review, 120(3), 512.
Bolton, G. E., & Ockenfels, A. (2005). A stress test of fairness measures in models of social utility. Economic Theory, 24(4), 957–982.
Busemyer, J. R., & Towsend, J. T. (1993). Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100(3), 432.
Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction. Princeton: Princeton Univ. Press.
Camerer, C., Lowenstein, G., & Rabin, M. (Eds.). (2004a). Advances in behavorial economics. Princeton: Princeton Univ. Press.
Camerer, C., et al. (2004b). Foundations of human sociality: Economic experiments and ethnographic evidence from fifteen small-scale societies. Oxford: Oxford University Press.
Castagnoli, E., & LiCalzi, M. (1996). Expected utility without utility. Theory and Decision, 41, 281–301.
Colman, A. M. (2003). Cooperation, psychological game theory, and limitations of rationality in social interaction. Behavioral and Brain Sciences, 26, 139–198.
Cowell, R. G., Dawid, A. P., Lauritzen, S. L., & Spiegelhalter, D. J. (1999). Probabilistic networks and expert systems. New York: Springer.
Cozman, F. G. (2000). Credal networks. Artificial Intelligence, 120, 199–233.
de Finetti, B. (1937). La prévision: ses lois logiques, ses sources subjectives. Annales de l’Institut Henri Poincaré 7:1–68 (translated as ‘Forsight. Its Logical Laws, Its Subjective Sources’, in Studies in Subjective Probability, H. E. Kyburg Jr. and H. E. Smokler (eds.), Wiley, New York, NY, 1964, pages 93–158).
Dufwenberg, M., & Kirchsteiger, G. (2004). A theory of sequential reciprocity. Games and Economic Behavior, 47, 268–298.
Dyer, J. S., & Sarin, R. K. (1979). Measurable multiattribute value functions. Operations Research, 27, 810–822.
Elster, J. (Ed.), (1985). The multiple self. Cambridge: Cambridge University Press.
Fehr, E., & Schmidt, K. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114, 817–868.
Fishburn, P. C. (1973). The theory of social choice. Princeton: Princeton University Press.
Geanakoplos, J., Pearce, D., & Stacchetti, E. (1989). Psychological games and sequential rationality. Games and Economic Behavior, 1, 60–79.
Gilbert, M. (2008). Social convention revisited. Topoi, 27, 5–16.
Gilboa, I., & Schmeidler, D. (1988). Information dependent games. Economics Letters, 27, 215–221.
Hansson, B. (1972). The independence condition on the theory of social choice, working paper no. 2, The Mattias Fremling Society, Department of Philosophy, Lund.
Harsanyi, J. (1955). Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Journal of Political Economy, 63, 315.
Henrich, J., et al. (2005). “Economic Man” in cross-culturative perspective: Behavorial experiments in 15 small-scale societies. Behavioral and Brain Sciences, 28(6), 795–855.
Hicks, J. R. (1939). Foundations of welfare economics. Economic Journal, 49(196), 696–712.
Hollis, M. (1998). Trust within reason. Cambridge: Cambridge University Press.
James, W. (1956). The will to believe and other essays. New York: Dover.
Jensen, F. V. (2001). Bayesian networks and decision graphs. New York: Springer.
Kaldor, N. (1939). Welfare propositions of economic and interpersonal comparisons of utility. Economic Journal, 49(195), 549–552.
Keeney, R. L., & Raiffa, H. (1976). Decisions with multiple objectives. Cambridge: Cambridge University Press.
Kemeny, J. (1955). Fair bets and inductive probabilities. Journal of Symbolic Logic, 20(1), 251–262.
Lam, S. W., Ng, T. S., Sim, M., & Song, J. H. (2013). Multiple objective satisficing under uncertainty. Operations Research, 61, 214–217.
Landau, M., & Chisholm, D. (1995). The arrogance of optimism: Notes on failure-avoidance management. Journal of Contingencies and Crisis Management, 3, 67–80.
Lehman, R. S. (1955). On conformation and rational betting. Journal of Symbolic Logic, 20(1), 263–273.
Levi, I. (1980). The Enterprise of Knowledge. Cambridge: MIT Press.
Margolis, H. (1990). Dual utilities and rational choice. In J. Mansbridge (Ed.), Beyond self-interest, chap 15 (pp. 239–253). Chicago Il: University of Chicago Press.
Murray, J.A.H., Bradley, H., Craigie, W.A., & Onions, C.T. (Eds.). (1991). The compact oxford english dictionary. Oxford: The Oxford Univ. Press.
Nash, J. F. (1950). The bargaining problem. Econometrica, 18, 155–162.
Nash, J. F. (1951). Non-cooperataive games. Annals of Mathematics, 54, 289–295.
von Neumann, J., & Morgenstern, O. (1944). The theory of games and economic behavior. Princeton: Princeton University Press. (2nd ed., 1947).
Palmer, F. R. (1971). Grammar. Harmondsworth: Penguin.
Pazgal, A. (1997). Satisficing leads to cooperation in mutual interests games. International Journal of Game Theory, 26(4), 439–453.
Pearl, J. (1988). Probabilistic reasoning in intelligent systems. San Mateo: Morgan Kaufmann.
Popper, K. R. (1963). Conjectures and refutations: The growth of scientific knowledge. New York: Harper & Row.
Ramsey, F. P. (1978). Truth and probability. In D. H. Mellor (Ed.), Foundations: Essays in philosophy, logic, mathematics, and economics (pp. 58–100). Atlantic Highlands: The Humanities Press.
Rawls, J. (1971). A theory of justice. Cambridge: Harvard University Press.
Ross, D. (2014). Theory of conditional games. Journal of Economic Methodology, 21, 193–198.
Scitovsky, T. (1941). A note on welfare propositions in economics. Review of Economic Studies, 9(1), 77–88.
Sen, A. K. (1990). Rational fools: A critique of the behavorial foundations ofeconomic theory. In J. J. Mansbridge (Ed.), Beyond self-interest, chap 2 (pp. 25–43). Chicago, Il: University ofChicago Press.
Shubik, M. (1982). Game theory in the social sciences. Cambridge: MIT Press.
Simon, H. A. (1955). A behavioral model of rational choice. Quarterly Journal of Economics, 59, 99–118.
Simon, H.A. (1982). The role of expectations in an adaptive or behavioristic model. In: Models of Bounded Rationality, vol 2 (pp 380–399). Cambridge: MIT Press.
Steedman, I., & Krause, U. (1985). Goethe’s Faust, arrow’s possibility theorem and the individual decision maker. In J. Elster (Ed.), The multiple self, chap 8 (pp. 197–231). Cambridge: Cambridge University Press.
Stirling, W. (2012). Theory of conditional games. Cambridge: Cambridge University Press.
Stirling, W. C. (2003). Satisficing games and decision making: With applications to engineering and computer science. Cambridge: Cambridge University Press.
Stirling, W. C., & Felin, T. (2013). Game theory, conditional preferences, and socialinfluence. PLoS One, 8(2), e56,751. doi:10.1371/journal.pone.0056,751.
Sugden, R. (1993). Thinking as a team: Towards an explanation of nonselfish behavior. Social Philosophy and Policy, 10, 69–89.
Sugden, R. (2000). Team preferences. Economics and Philosophy, 16, 175–204.
Sugden, R. (2003). The logic of team reasoning. Philosophical Explorations, 6, 165–181.
Unger, P. (1975). Ignorance: a case for skepticism. Oxford: Oxford University Press.
Whitehead, A. N. (1937). Adventures in ideas. London: Macmillan.
Author information
Authors and Affiliations
Corresponding author
Appendix: Proof of the isomorphism lemma
Appendix: Proof of the isomorphism lemma
Lemma 2
Subjugation is isomorphic to sure loss.
Proof
To establish this result we first prove that the categorical and conditional utilities are order isomorphic to marginal and conditional probability mass functions. Without loss of generality, let us restrict attention to a two-agent collective \(\{Z_1,Z_2\}\), with \(Z_1\) possessing a categorical utility \(u_{{\scriptscriptstyle Z_1}} \text{: }\ {{\mathcal {A}}}_1\times {{\mathcal {A}}}_2 \rightarrow [0,1]\) and \(Z_2\) possessing a family of conditional utilities \(\{u_{{\scriptscriptstyle Z_2}|{\scriptscriptstyle Z_1}}(\cdot | z_1, z_2) \text{: }\ \rightarrow [0,1]\ \forall \ (z_1, z_2) \in {{\mathcal {A}}}_1 \times {{\mathcal {A}}}_2\}\). To proceed, let \(\varOmega _1\) and \(\varOmega _2\) be arbitrary probability sample spaces of distinct elements and cardinality equal to the cardinality of \({{\mathcal {A}}}_1\) and \({{\mathcal {A}}}_2\), respectively, and let \(\{Y_1, Y_2\}\) be discrete bijective function (random variables in statistical parlance) defined over \(\varOmega _1 \times \varOmega _2\) such that \(Y_1\) possesses a probability mass function \(p_{{\scriptscriptstyle Y_1}}\) over \(\varOmega _1\times \varOmega _2\) and \(Y_2\) possesses a family of conditional probability mass functions \(\{ p_{{\scriptscriptstyle Y_2}|{\scriptscriptstyle Y_1}}(\cdot | \omega _1, \omega _2) \text{: }\ \varOmega _1 \times \varOmega _2 \rightarrow [0,1] \ \forall (\omega _1, \omega _2) \in \varOmega _1 \times \varOmega _2 \}\). Now let \(g \text{: }\ {{\mathcal {A}}}_1\times {{\mathcal {A}}}_2 \rightarrow \varOmega _1\times \varOmega _2\) be a bijective mapping of the form \(g(z_1,z_2) = (\omega _1,\omega _2) \in \varOmega _1 \times \varOmega _2\). Define g such that
for all \((z_1,z_2) \in {{\mathcal {A}}}_1\times {{\mathcal {A}}}_2\), and
for all \((z_1^\prime , z_2^\prime ) \in {{\mathcal {A}}}_1\times {{\mathcal {A}}}_2\). It is immediate that this mapping establishes the structural equivalence of the benefit criterion regarding \({{\mathcal {A}}}_1\times {{\mathcal {A}}}_2\) and the belief criterion regarding \(\varOmega _1 \times \varOmega _2\). It remains to confirm that \(Z_2\) computing its utility of \((z_1,z_2)\) given that \(Z_1\) conjectures \((z_1^\prime , z_2^\prime )\) is equivalent to \(Y_2\) computing its belief that \(g(z_1,z_2)\) is realized given that \(Y_1\) asserts that \(g(z_1,z_2)\) is realized. To establish this equivalence, we simply observe that the conjecture by \(Z_1\) and the realization assertion by \(Y_1\) are both antecedents of hypothetical propositions whose consequents are \(u_{{\scriptscriptstyle Z_2}|{\scriptscriptstyle Z_1}}(z_1, z_2|z_1^\prime ,z_2^\prime )\) and \(p_{{\scriptscriptstyle Y_2}|{\scriptscriptstyle Y_1}}[g(z_1,z_2) | g(z_1^\prime ,z_2^\prime )]\), respectively. This establishes the order isomorphism.
To establish the isomorphism between subjugation and sure loss, let \(\{Y_1, Y_2\}\) be a collective of discrete random variables, each defined over the product sample space \({\varvec{\varOmega }}= \varOmega _1 \times \varOmega _2\). Let \(p_{{\scriptscriptstyle Y_i}} \text{: }\ {\varvec{\varOmega }}\rightarrow \mathbb {R}\) be a belief function (not necessarily a probability) such that \(p_{{\scriptscriptstyle Y_i}} ({\varvec{\omega }}) \ge p_{{\scriptscriptstyle Y_i}} ({\varvec{\omega }}^\prime )\) means that the belief that \({\varvec{\omega }}\) will be realized is at least as great as the belief that \({\varvec{\omega }}^\prime \) will be realized. Also, let \(p_{{\scriptscriptstyle Y_1}{\scriptscriptstyle Y_2}} \text{: }\ {\varvec{\varOmega }}^2 \rightarrow \mathbb {R}\) be a belief function such that \(p_{{\scriptscriptstyle Y_1}{\scriptscriptstyle Y_2}}({\varvec{\omega }}_1, {\varvec{\omega }}_2) \ge p_{{\scriptscriptstyle Y_1}{\scriptscriptstyle Y_2}}({\varvec{\omega }}_1^\prime ,{\varvec{\omega }}_2^\prime )\) means that the belief that \(({\varvec{\omega }}_1, {\varvec{\omega }}_2)\) is realized is at least as great as the belief that \(({\varvec{\omega }}_1^\prime , {\varvec{\omega }}_2^\prime )\) is realized.
Suppose there exists \({\varvec{\omega }}_1^* \in {\varvec{\varOmega }}\) such that
and that
for all \( {\varvec{\omega }}_1 \in {\varvec{\varOmega }}{\setminus } \{{\varvec{\omega }}_1^*\}\) and for all \({\varvec{\omega }}_2\in {\varvec{\varOmega }}\). Thus, even though \({\varvec{\omega }}_1^*\) is \(Y_1\)’s most strongly believed event, the belief regarding the realization of any joint event for which \(\omega _1^*\) is \(Y_1\)’s realization is weaker than the belief regarding the realization of the corresponding joint event with any other \({\varvec{\omega }}_1\) as \(Y_1\)’s realization.
If, on the basis of (40) one were to enter a lottery to earn $1 if \({\varvec{\omega }}_1^*\) is realized, a fair entry fee would be \(q_1 > \frac{1}{2}\). On the other hand, if, on the basis of (41), one were to earn $1 if \({\varvec{\omega }}_1^*\) is not realized, then a fair entry fee would be \(q_2 > \frac{1}{2}\). By combining bets, one would be certain of winning $1 with a fair entry fee of \(q_1 + q_2>1\), therefore resulting in a sure loss.
It is immediate that the relationships given by (13) and (40) and by (14) and (41) are identical. Thus, sure loss is isomorphic to subjugation. \(\square \)
Rights and permissions
About this article
Cite this article
Stirling, W.C., Felin, T. Satisficing, preferences, and social interaction: a new perspective. Theory Decis 81, 279–308 (2016). https://doi.org/10.1007/s11238-015-9531-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-015-9531-y