[Social choice lottery rules are analyzed for two-candidate elections with voters who may be uncertain about whom they prefer. A voter's uncertainty is reflected by a nonobservable choice probability of voting for candidate A rather than candidate B, given that he votes. Lottery rules are based on the votes for A and B; they are to be monotonic and symmetric in voters and in candidates. Given n voters, all lottery rules are convex combinations of about n/2 basic rules ranging from the coin-flip rule to simple majority. Candidate A's win probability and two measures of expected voter satisfaction are examined as functions of the individuals' choice probabilities and the lottery rules. Comparisons are made between simple majority and the proportional lottery rule which assigns social choice probability of j/n to A when A gets j of n votes. Each of simple majority and the proportional lottery rule satisfies attractive properties that are not satisfied by the other rule.]

The presence or absence of seasonal influences on interest rates is an important issue both for policy (Gibson, 1970) and for estimation of monetary relationships (Lombra and Kaufman, 1975). Thus conflict between recent research findings of Barth and Bennett (1975) (hereafter B-B) in this REVIEW and previous work is unsettling.' B-B examined two sets of data: (a) monthly observations on several interest rate series over period 1947-1970, and (b) daily observations on 90-day Treasury bill rate from May 1961 to December 1965. Using monthly dummy variables they concluded that seasonal effects do not appear to be present in interest rates examined. However, daily observations do yield significant seasonal effects for short term Treasury rate. B-B resolve this conflict by suggesting that the process of averaging daily data into monthly arithmetic means reduces variation in interest rate enough that one cannot detect (1975, p. 82). In what follows we reformulate their model in a framework consistent with problems noted by Bagshaw and Phaup (1977) and Bolch and Huang (1977).2 Our results using monthly data from April 1951 to March 1973 indicate statistically significant seasonal influences. Moreover, we demonstrate that averaging a data series will not eliminate seasonal pattern underlying B-B model. Thus B-B explanation of conflict of their results with daily and monthly data is not appropriate.3 The method selected for estimating seasonal components of an economic time series will depend on definition selected for seasonality.4 B-B's findings are relevant to only one such definition and implicitly assume one can model seasonal influences on interest rates independently from modeling of process of change in rates themselves.5 Accordingly discrepancy with past evidence supporting seasonality may be result of these factors. To illustrate this point we have selected an amended model consistent with Barth and Bennett's own suggestions (1975, p. 80, fn. 2) and following Nelson's (1970) analysis of term structure of interest rates. Equation (1) defines our model:

Recent studies at both the theoretical and empirical levels (Feldstein and Rothschild, 1974, Nickell, 1975, Feldstein and Foot, 1971, Eisner, 1972 and Bitros and Kelejian, 1974) have offered accumulating evidence inconsistent with the neoclassical investment theory assumption that replacement investment is a constant fraction of the capital stock.' While this assumption was accepted largely on theoretical grounds, with renewal theory implying in the long run (given capital growing at a constant rate) that replacement investment will approach a constant proportion of capital stock, Feldstein and Rothschild have recently presented a series of contrasting theoretical arguments that suggest that it is likely to be untenable. To date, the most conclusive set of empirical results in support of this view has been Bitros and Kelejian's (hereafter B-K) analysis using annual data for the U.S. electric utility industry for the period 1946 to 1971. Unfortunately, the B-K analysis is subject to several important problems which involve the measurement of capacity and the nature of the electric utility industry.2 The purpose of this paper is to re-examine the B-K results, accounting for each of these issues. Given the importance of the proportionality assumption of neoclassical investment theory (particularly in the development of capital stock and user cost series), a reconsideration of the B-K evidence is warranted. Section II briefly reviews the B-K model, data, and results. The third section outlines each of the problems with their analysis. In section IV we present estimates of an amended version of their model using a relatively homogeneous component of the electric power industry, class A and B privately-owned firms for the period 1946 to 1971. Furthermore, we test this model for specifications errors and compare our findings with those of B-K. The last section summarizes the results.

Charles J. Cicchetti, Anthony C. Fisher, V. Kerry Smith, An Econometric Evaluation of a Generalized Consumer Surplus Measure: The Mineral King Controversy, Econometrica, Vol. 45, No. 4 (May, 1977), p. 1041