Risk-preference in coin-toss games

It is hypothesized that an individual has a preferred unidimensional risk level in a coin-tossing game, and that his preferences are single-peaked over the risk scale. Risk was varied by increasing both the monetary denomination (D = le to $1) and number of tosses (N = 1 to 20) involved in a game. The rank order preference data of 30 subjects within sets of games having either constant D or N, single stimulus preference data, and pair comparison preferences between games supported these hypotheses. Data also supported the existence of a function R,[(D, N)] which maps games onto the risk scale and is monotone increasing in both arguments. However, the exact form of the function may vary, depending on the particular set of games from which the subject chooses. The prevailing expectation theories of individual decision making in a risky situation (Edwards, 1954, 1955) all avoid the subjective variable of riskiness. However, this variable has been given some attention as a stimulus dimension relevant to choice (Coombs and Pruitt, 1960; Royden, Suppes, and Walsh, 1959). In these experimental studies, the variance or some other parameter of the frequency distribution of a game’s possible outcomes was explored as a potential correlate of risk. The evidence supports the hypothesis that variance is a strong correlate of risk in simple game situations, but in more complex situations, the concept of risk is elusive and idiosyncratic (Wilcox, 1967). Thus we have chosen to treat the concept of risk as being undefined in a strict sense, although we do assume the existence of a variable which, in addition to expected value, mediates preferences in a consistent manner, can be experimentally manipulated in various ways, and for intuitive reasons might be identified as risk. The present study considers a number of coin-tossing games which vary in two aspects: the coin denomination (D) involved in a single toss, and the number of tosses (N) composing the complete game. As an example, the game (25@,5) represents a game in which 5 quarters are tossed all at once. For each coin landing heads, the game’s owner is paid a quarter by a bank. For each tail, the bank is paid a quarter by the owner.