On a Problem of Estimation Occurring in Public Opinion Polls
Henry B. Mann · The Annals of Mathematical Statistics · 1945
To a.rrive at an estimate of the number of electoral votes that will be cast for a presidential candidate a poll is taken of XiN interviews in the ith state (i = 1, ^, 48) where the Xi are fixed constants > 0 such that 2Xi = 1 and the respondent is asked for which candidate he intends to cast his vote. To estimate the number of electoral votes wvhich candidate A will receive, the electoral votes of all the states in which the poll shows a majority for candidate A are added and their sum is used as an estimate for the number of electoral votes which candidate A will receive. In this paper certain properties of this estimate will be discussed. It will be showvn that it is a biased but consistent estimate and an upper bound for the bias vill be derived. Finally we shall derive that distribution of interviews which minimizes the variance of our estimate. In all that follows we shall consider the poll as a random or stratified random sample and shall disregard the bias introduced by inaccurate answers. Our results however remain valid as long as the sampling variance is proportional 1 to .