The Weights of Evidence

Abstract

Dale A. Nance it will always increase its "weight." . . . [W]eight, to speak metaphorically, measures the sum of the favourable and unfavourable evidence, probability measures the difference (Keynes 1921, 71, 77).Keynes's point readily generalizes to any theory about the convincing force of evidence, whether or not articulated in terms of probabilities and, if so, whether or not based on the particular "logical" theory of probability that Keynes endorsed. 1 Weight in the first sense is the degree to which a rational decision-maker is convinced of the truth of a proposition as compared to some competing hypothesis (which could be simply that the proposition is false). It is a function of the extent to which available evidence interlocks to form a sound explanatory account favoring the proposition over the competing hypothesis (Haack 1993, ch. 4). But this degree of weight can be based on a relatively thin mass of evidence or a relatively rich one, the difference between which concerns weight in the second sense. Weight in the latter sense depends on the relative completeness of evidence, the extent to which the evidence addresses the important inferential questions that are raised by the competing hypotheses, including questions of the reliability of the items of evidence considered (Stein 2005, 91-106). Again, an increase in weight in the second sense can increase, decrease, or leave unchanged the weight of the evidence in the first sense.An abstract example will add precision. From a baseline of given evidence with regard to a proposition and a competing hypothesis, consider the effect of conducting a test for which a positive result supports the proposition and a negative result supports the competing hypothesis. Obtaining some result (without regard to its value) is what increases weight in the Keynesian sense, but it has an indeterminate effect on convincing force. Conversely, which value is obtained (positive or negative) is what affects convincing force, but it has no effect on Keynesian weight. Notice that Keynesian weight is subject to the decision-maker's control in a sense that convincing force is not. Within practical limits, Keynesian weight can be chosen, provided the decision-maker has the capacity to cause such tests to be conducted, whereas for a given level of Keynesian weight, convincing force can only be assessed (assuming of course that the decision-maker does not independently control the test result).These two dimensions of evidence are fundamental to decision-making under conditions of uncertainty. Someone contemplating action faces two decisions that correspond to these two senses of weight. When a certain action is desirable if and only if some proposition is true, then one's choice depends on the convincing force of the available evidence regarding its truth. (For example, the truth or falsity of the proposition might affect the expected total utility of the action.) But that decision can be displaced by a second: the decision whether to decide about the contemplated act based on the ava...

Deliberation and confidence change

“…3 Our conception of confidence thus differs from that of authors who use "confidence", "credence", or "degree of belief" synonymously (Lasonen-Aarnio 2013), or who take confidence as a betting disposition or affective state that is explained or determined by credence (Christensen 2009;Frances and Matheson 2019). It might turn out that confidence is related or can even be reduced to resistance to revision (Levi 1980), credal resilience (Skyrms 1977;Egan and Elga 2005), higher-order uncertainty (Dorst 2019(Dorst , 2020, or evidential weight (Nance 2008;Joyce 2005), yet these questions are not our concern in the present paper.…”

Here is a table: A prolegomenon to a future new evidence scholarship in Africa

“…Rptr. 497 (1968)) in the identification of the robber of the elderly complainant's purse, and the subsequent suggestions that Bayesian analysis could be a viable solution in this regard (Brilmayer, 1986; Finkelstein and Fairly, 1970; Friedman, 1986; Kaye, 1986; Nance, 2008: 267; Nance, 2016; Schum, 2002: 145; Walker, 2002: 197). A small group of sceptics, led by Tribe, began to emerge in the second wave in resistance against this early wave of ‘trial by mathematics’ (Allen, 1986: 401; Tribe, 1971: 1329).…”

(Im)probable stories

“…Perhaps the burden to ensure that our set of scenarios is good enough should be placed at the feet of investigators. Alternatively, writing in the context of the American system where the fact-finder is the jury, Nance (2008) suggests that the decision whether the available set of evidence is sufficiently complete for the case to go to trial lies with the judge in the case. Whether we suspect unconceived alternatives could be part of this decision.…”

“…This argument will act as the foil for my own position. It combines insights from, among others, the work of Dale Nance (2008;, Larry Laudan (2006) and Amalia Amaya (2009). The argument begins with the observation that, when we are faced with potential missing evidence, a reasonable response is to gather further information (to the extent that this is cost-effectively possible) (Nance, 2008;.…”

“…It combines insights from, among others, the work of Dale Nance (2008;, Larry Laudan (2006) and Amalia Amaya (2009). The argument begins with the observation that, when we are faced with potential missing evidence, a reasonable response is to gather further information (to the extent that this is cost-effectively possible) (Nance, 2008;. In criminal cases this 'burden of production' will typically fall on the prosecution, unless the defendant has sole access to the missing evidence (Nance, 2008, 278).…”