The main differences that I see between EDT and CDT are, first, that EDT is misnamed. The equations do not use “evidence” in the common sense meaning of that term. They use it in the way people deploying statistics tend, erroneously, to use it—as presuming causes when the only valid interpretation of the numbers treats them as correlations. The probability of B, given A, P(B|A), can be due to A causing B (which is how we are to understand the arrow in Bell’s equations in Appendix 1); B causing A; C causing both; A and B happening in periodic cycles that tend to align (e.g. monthly menstruation and full moons); A and B being in part-whole relationships; in container-contained relationships; and many many other correlated relationships; or due to various combinations thereof. Given all of such possible relationships, it then becomes a mistake to believe that doing A will result in (e.g. cause) B, just because the probability of event B occurring, given that A has occurred, is high. The problem is well-illustrated by the fallaciousness of the reasoning in EDT that recommends that politicians kiss babies, given the set up supposed in Bell’s example.
The second major difference, brought out by the first, is that standard statistical treatments of probabilities are based on frequencies, rather than propensities, as interpretations of the numbers. As such, the assumptions made in such theories work well in depicting areas of investigation that are like tosses of dice, drawing cards, pulling balls from urns, and so on, but tend to go awry when trying to depict causation, or isolate signals from noise in real cases, as when conceptually ill-equiped investigators think that, because they have found a reliable correlation, they have found a causal influence rather than a correlation due to noise. For example, in order to establish a good p-value, they compare their results to what would happen under a random distribution, and treat the resulting p-value as a good basis on which to claim they have established a prima facie case (a “finding”) that A “influences” B. The problem is that showing that a correlation isn’t due to random distribution doesn’t show much. Given all the other options mentioned above, all of which are potentially part of the background noise, what investigators need for their stronger claims is a comparison with a natural distribution, which tends not to be random, and contains all the potential confounders that explain the correlation differently.
This should, I hope, bring out some of what is at issue here. Decision theory, ideally, gives precise symbolic form and apt guidance for decision making dilemmas. But to do so, it needs its numeric and symbolic representations to be good maps of the terrain, which they aren’t, yet, if “EDT” is being used. In short, if you can ignore causation, and causation’s arrow, EDT will suit you fine. The problem is that most of the time you can’t.
The main differences that I see between EDT and CDT are, first, that EDT is misnamed. The equations do not use “evidence” in the common sense meaning of that term. They use it in the way people deploying statistics tend, erroneously, to use it—as presuming causes when the only valid interpretation of the numbers treats them as correlations. The probability of B, given A, P(B|A), can be due to A causing B (which is how we are to understand the arrow in Bell’s equations in Appendix 1); B causing A; C causing both; A and B happening in periodic cycles that tend to align (e.g. monthly menstruation and full moons); A and B being in part-whole relationships; in container-contained relationships; and many many other correlated relationships; or due to various combinations thereof. Given all of such possible relationships, it then becomes a mistake to believe that doing A will result in (e.g. cause) B, just because the probability of event B occurring, given that A has occurred, is high. The problem is well-illustrated by the fallaciousness of the reasoning in EDT that recommends that politicians kiss babies, given the set up supposed in Bell’s example.
The second major difference, brought out by the first, is that standard statistical treatments of probabilities are based on frequencies, rather than propensities, as interpretations of the numbers. As such, the assumptions made in such theories work well in depicting areas of investigation that are like tosses of dice, drawing cards, pulling balls from urns, and so on, but tend to go awry when trying to depict causation, or isolate signals from noise in real cases, as when conceptually ill-equiped investigators think that, because they have found a reliable correlation, they have found a causal influence rather than a correlation due to noise. For example, in order to establish a good p-value, they compare their results to what would happen under a random distribution, and treat the resulting p-value as a good basis on which to claim they have established a prima facie case (a “finding”) that A “influences” B. The problem is that showing that a correlation isn’t due to random distribution doesn’t show much. Given all the other options mentioned above, all of which are potentially part of the background noise, what investigators need for their stronger claims is a comparison with a natural distribution, which tends not to be random, and contains all the potential confounders that explain the correlation differently.
This should, I hope, bring out some of what is at issue here. Decision theory, ideally, gives precise symbolic form and apt guidance for decision making dilemmas. But to do so, it needs its numeric and symbolic representations to be good maps of the terrain, which they aren’t, yet, if “EDT” is being used. In short, if you can ignore causation, and causation’s arrow, EDT will suit you fine. The problem is that most of the time you can’t.