Academic journal article International Journal of Comparative Sociology

War: Long Range Time Series by Conditioning

Academic journal article International Journal of Comparative Sociology

War: Long Range Time Series by Conditioning

Article excerpt

Introduction

There are two purposes to this paper. The fIrst purpose is to present a set of six basic time series of war 35,000 B.C. to present day, The time series are one substantive result of a larger methodological project the objective of which was to develop a general method for constructing long range time series of culture and society (Denton, 1993a). The second purpose of the present paper is to build on Denton (1993a) by clarifying a variety of assumptions required by the method and also by presenting empirical evidence that time series constructed by the method will customarily have good fit to the empirical world.

A Method for Constructing Long Range Time Series of War

We need to start with a summary of the method for constructing long range time series by conditioning. For reason of space limitations what follows is only a summary. For a more leisurely development of the method (including a variety of tables) see Denton (1993a). Let us start by defining the individual as the unit of analysis. Define discrete random variables X, X=1,2... and Y, Y = 1,2,3. The unconditional probability P([E.sub.1]) of the event, say, that X=x, may be computed (Ross, 1989:93-108) by conditioning on Y

P(X=x)= [summation over Y]P(X=x [where] Y=y)P(Y=y) (1)

Conditioning will be used here to calculate P(X=x) because conditional probabilities P(X=x [where] Y=y) are easier to obtain than unconditional probabilities P(X=x). Although only discrete random variables are used in this paper the method may be extended to continuous random variables.

Now let us assign substantive meaning to the conditioning random variable Y, Y=1,2,3. Define the discrete conditioning random variable Y, Y=1,2,3 as having values Y=1 (the individual lives in a non-state primarily non-food producing society), Y=2 (the individual lives in a non-state primarily food producing society) or Y=3 (the individual lives in a state primarily food producing society). The probabilities P(Y=y), y=1,2,3 for the conditioning random variable Y, Y=1,2,3 are observable in the archaeological record of each of 10 world regions (see Denton, 1993a for the table of regional probabilities and how they were obtained). The conditional probabilities P(X=x [where] Y=y) are estimatable (below) from a suitable cross-cultural ethnographic data base. Although P(Y=y), y=1,2,3 varies over time and by region it is assumed, for reasons stated below, that for fixed Y=y, y=1,2,3 and fixed X=x, x=1,2,... P(X=x [where] Y=y) is invariant over time and space. We will assign substantive meaning to random variable, X, X=1,2,... shortly. As described in Denton (1993a) estimates of regional probabilities P(Y=y) are made for each of the 10 world regions for each of 38 equally spaced time points 35,000 B.C. to 2,000 A.D. so as to span the era of the modern form of our species. As a result, we have most of the information needed in order to use Equation (1) to estimate P(X=x) at a time point - regional P(Y=y) from the archaeological record, P(X=x [where] Y=y) from the cross-cultural data base.

Denton (1993a) provides a table of estimates of world populations of individuals by region and over time. If an unconditional regional estimate P(X=x) obtained directly from Equation (1) at a time point is multiplied by an estimate of the regional population n at the time point we obtain nP(X=x) which is an estimate of the expected population of individuals characterizable X=x in the region at the time point. Summing expected regional populations across a time point (Denton, 1993a) yields an expected world population characterizable X=x at the time point. The proportion of individuals characterizable X=x in the world at a time point may be thought of as the probability that an individual was characterizable X=x at the time point. This probability may also be attained directly by simply plugging world P(Y=y) into Equation (1). This latter world P(Y=y) is obtainable by summing expected regional populations characterizable Y=y, y=1,2,3 across each time point and then expressing the sum as a proportion of the total world population at the time point. …

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