1) It’s a one-player game where you strictly prefer a randomized strategy to any deterministic one. This is similar to the AMD problem, and impossible if you’re making decisions using Bayesian probability.
Having a random-number generator is equivalent to having a certain very restricted kind of memory.
For example, if you have a pseudo-random number generator in a computer, then the generator requires a seed, and this seed cannot be the same every day. The change of the seed from day to day constitutes a trace in the computer of the days’ passing. Therefore, you and the computer, taken together, “remember”, in a certain very restricted sense, the passing of the days. Fortunately, this restricted kind of memory turns out to be just enough to let you do far better than you could have done with no memory at all. (I gave this argument in slightly more detail in this old comment thread.)
So, the presence of a random-number generator is just a weakening of the requirement of complete amnesia. However, given this restricted kind of memory, you are making your decisions in accordance with Bayesian probability theory. [ETA: I misunderstood cousin_it’s point when I wrote that last sentence.]
However, given this restricted kind of memory, you are making your decisions in accordance with Bayesian probability theory.
It seems to me that if you have a coin, your probability distribution on envelopes should still depend on the strategy you adopt, not just on the coin. Are you sure you’re not sneaking in “planning-optimality” somehow? Can you explain in more detail why the decision on each day is separately “action-optimal”?
I think I misunderstood what you meant by “impossible if you’re making decisions using Bayesian probability.” I wasn’t trying to avoid being “planning-optimal”. It is not as though the agent is thinking, “The PRNG just output 0.31. Therefore, this envelope is more likely to contain the money today.”, which I guess is what “action-optimal” reasoning would look like in this case.
When I said that “you are making your decisions in accordance with Bayesian probability theory”, I meant that your choice of plan is based on your beliefs about the distribution of outputs generated by the PRNG. These beliefs, in turn, could be the result of applying Bayesian epistemology to your prior empirical experience with PRNGs.
Yeah. It looks like there’s a discontinuity between using a RNG and having perfect memory. Perfect memory lets us get away with “action-optimal” reasoning, but if it’s even a little imperfect, we need to go “planning-optimal”.
You are mistaken in your conception of memory as it relates to the field of statistics.
“Episodic and semantic memory give rise to two different states of consciousness, autonoetic and noetic, which influence two kinds of subjective experience, remembering and knowing, respectively.[2] Autonoetic consciousness refers to the ability of recovering the episode in which an item originally occurred. In noetic consciousness, an item is familiar but the episode in which it was first encountered is absent and cannot be recollected. Remembering involves retrieval from episodic memory and knowing involves retrieval from semantic memory.[2]
In his SPI model, Tulving stated that encoding into episodic and semantic memory is serial, storage is parallel, and retrieval is independent.[2] By this model, events are first encoded in semantic memory before being encoded in episodic memory; thus, both systems may have an influence on the recognition of the event.[2]
High Threshold Model
The original high-threshold model held that recognition is a probabilistic process. [5] It is assumed that there is some probability that previously studied items will exceed a memory threshold. If an item exceeds the threshold then it is in a discrete memory state. If an item does not exceed the threshold then it is not remembered, but it may still be endorsed as old on the basis of a random guess.[6] According to this model, a test item is either recognized (i.e., it falls above a threshold) or it is not (i.e., it falls below a threshold), with no degrees of recognition occurring between these extremes.[5] Only target items can generate an above-threshold recognition response because only they appeared on the list.[5] The lures, along with any targets that are forgotten, fall below threshold, which means that they generate no memory signal whatsoever. For these items, the participant has the option of declaring them to be new (as a conservative participant might do) or guessing that some of them are old (as a more liberal participant might do).[5] False alarms in this model reflect memory-free guesses that are made to some of the lures.[5] This simple and intuitively appealing model yields the once widely used correction for guessing formula, and it predicts a linear receiver operating characteristic (ROC). An ROC is simply a plot of the hit rate versus the false alarm rate for different levels of bias. [5] A typical ROC is obtained by asking participants to supply confidence ratings for their recognition memory decisions.[5] Several pairs of hit and false alarm rates can then be computed by accumulating ratings from different points on the confidence scale (beginning with the most confident responses). The high-threshold model of recognition memory predicts that a plot of the hit rate versus the false alarm rate (i.e., the ROC) will be linear it also predicts that the z-ROC will be curvilinear.[5]
Dual-process accounts
The dual-process account states that recognition decisions are based on the processes of recollection and familiarity.[5] Recollection is a conscious, effortful process in which specific details of the context in which an item was encountered are retrieved.[5] Familiarity is a relatively fast, automatic process in which one gets the feeling the item has been encountered before, but the context in which it was encountered is not retrieved.[5] According to this view, remember responses reflect recollections of past experiences and know responses are associated with recognition on the basis of familiarity.[7]
Signal-detection theory
According to this theory, recognition decisions are based on the strength of a memory trace in reference to a certain decision threshold. A memory that exceeds this threshold is perceived as old, and trace that does not exceed the threshold is perceived as new. According to this theory, remember and know responses are products of different degrees of memory strength. There are two criteria on a decision axis; a point low on the axis is associated with a know decision, and a point high on the axis is associated with a remember decision.[5] If memory strength is high, individuals make a “remember” response, and if memory strength is low, individuals make a “know” response.[5]
Probably the strongest support for the use of signal detection theory in recognition memory came from the analysis of ROCs. An ROC is the function that relates the proportion of correct recognitions (hit rate) to the proportion of incorrect recognitions (false-alarm rate).[8]
Signal-detection theory assumed a preeminent position in the field of recognition memory in large part because its predictions about the shape of the ROC were almost always shown to be more accurate than the predictions of the intuitively plausible high-threshold model. [5] More specifically, the signal-detection model, which assumes that memory strength is a graded phenomenon (not a discrete, probabilistic phenomenon) predicts that the ROC will be curvilinear, and because every recognition memory ROC analyzed between 1958 and 1997 was curvilinear, the high-threshold model was abandoned in favor of signal-detection theory.[5] Although signal-detection theory predicts a curvilinear ROC when the hit rate is plotted against the false alarm rate, it predicts a linear ROC when the hit and false alarm rates are converted to z scores (yielding a z-ROC).[5]
“The predictive power of the signal detection modem seems to rely on know responses being related to transient feelings of familiarity without conscious recollection, rather than Tulving’s (1985) original definition of know awareness. [9]
Dual-process signal-detection/high-threshold theory
The dual-process signal-detection/high-threshold theory tries to reconcile dual-process theory and signal-detection theory into one main theory. This theory states that recollection is governed by a threshold process, while familiarity is not.[5] Recollection is a high-threshold process (i.e., recollection either occurs or does not occur), whereas familiarity is a continuous variable that is governed by an equal-variance detection model.[5] On a recognition test, item recognition is based on recollection if the target item has exceeded threshold, producing an “old” response.[5] If the target item does not reach threshold, the individual must make an item recognition decision based on familiarity.[5] According to this theory, an individual makes a “remember” response when recollection has occurred. A know response is made when recollection has not occurred, and the individual must decide whether they recognize the target item solely on familiarity.[5] Thus, in this model, the participant is thought to resort to familiarity as a backup process whenever recollection fails to occur.[5]
Distinctiveness/fluency model
In the past, it was suggested that remembering is associated with conceptual processing and knowing is associated with perceptual processing. However, recent studies have reported that there are some conceptual factors that influence knowing and some perceptual factors that influence remembering.[2] Findings suggest that regardless of perceptual or conceptual factors, distinctiveness of processing at encoding is what affects remembering, and fluency of processing is what affects knowing.[2] Remembering is associated with distinctiveness because it is seen as an effortful, consciously controlled process.[2] Knowing, on the other hand, depends on fluency as it is more automatic and reflexic and requires much less effort.[2]”″
Having a random-number generator is equivalent to having a certain very restricted kind of memory.
For example, if you have a pseudo-random number generator in a computer, then the generator requires a seed, and this seed cannot be the same every day. The change of the seed from day to day constitutes a trace in the computer of the days’ passing. Therefore, you and the computer, taken together, “remember”, in a certain very restricted sense, the passing of the days. Fortunately, this restricted kind of memory turns out to be just enough to let you do far better than you could have done with no memory at all. (I gave this argument in slightly more detail in this old comment thread.)
So, the presence of a random-number generator is just a weakening of the requirement of complete amnesia. However, given this restricted kind of memory, you are making your decisions in accordance with Bayesian probability theory. [ETA: I misunderstood cousin_it’s point when I wrote that last sentence.]
It seems to me that if you have a coin, your probability distribution on envelopes should still depend on the strategy you adopt, not just on the coin. Are you sure you’re not sneaking in “planning-optimality” somehow? Can you explain in more detail why the decision on each day is separately “action-optimal”?
I think I misunderstood what you meant by “impossible if you’re making decisions using Bayesian probability.” I wasn’t trying to avoid being “planning-optimal”. It is not as though the agent is thinking, “The PRNG just output 0.31. Therefore, this envelope is more likely to contain the money today.”, which I guess is what “action-optimal” reasoning would look like in this case.
When I said that “you are making your decisions in accordance with Bayesian probability theory”, I meant that your choice of plan is based on your beliefs about the distribution of outputs generated by the PRNG. These beliefs, in turn, could be the result of applying Bayesian epistemology to your prior empirical experience with PRNGs.
Yeah. It looks like there’s a discontinuity between using a RNG and having perfect memory. Perfect memory lets us get away with “action-optimal” reasoning, but if it’s even a little imperfect, we need to go “planning-optimal”.
You are mistaken in your conception of memory as it relates to the field of statistics.
“Episodic and semantic memory give rise to two different states of consciousness, autonoetic and noetic, which influence two kinds of subjective experience, remembering and knowing, respectively.[2] Autonoetic consciousness refers to the ability of recovering the episode in which an item originally occurred. In noetic consciousness, an item is familiar but the episode in which it was first encountered is absent and cannot be recollected. Remembering involves retrieval from episodic memory and knowing involves retrieval from semantic memory.[2]
In his SPI model, Tulving stated that encoding into episodic and semantic memory is serial, storage is parallel, and retrieval is independent.[2] By this model, events are first encoded in semantic memory before being encoded in episodic memory; thus, both systems may have an influence on the recognition of the event.[2] High Threshold Model
The original high-threshold model held that recognition is a probabilistic process. [5] It is assumed that there is some probability that previously studied items will exceed a memory threshold. If an item exceeds the threshold then it is in a discrete memory state. If an item does not exceed the threshold then it is not remembered, but it may still be endorsed as old on the basis of a random guess.[6] According to this model, a test item is either recognized (i.e., it falls above a threshold) or it is not (i.e., it falls below a threshold), with no degrees of recognition occurring between these extremes.[5] Only target items can generate an above-threshold recognition response because only they appeared on the list.[5] The lures, along with any targets that are forgotten, fall below threshold, which means that they generate no memory signal whatsoever. For these items, the participant has the option of declaring them to be new (as a conservative participant might do) or guessing that some of them are old (as a more liberal participant might do).[5] False alarms in this model reflect memory-free guesses that are made to some of the lures.[5] This simple and intuitively appealing model yields the once widely used correction for guessing formula, and it predicts a linear receiver operating characteristic (ROC). An ROC is simply a plot of the hit rate versus the false alarm rate for different levels of bias. [5] A typical ROC is obtained by asking participants to supply confidence ratings for their recognition memory decisions.[5] Several pairs of hit and false alarm rates can then be computed by accumulating ratings from different points on the confidence scale (beginning with the most confident responses). The high-threshold model of recognition memory predicts that a plot of the hit rate versus the false alarm rate (i.e., the ROC) will be linear it also predicts that the z-ROC will be curvilinear.[5] Dual-process accounts
The dual-process account states that recognition decisions are based on the processes of recollection and familiarity.[5] Recollection is a conscious, effortful process in which specific details of the context in which an item was encountered are retrieved.[5] Familiarity is a relatively fast, automatic process in which one gets the feeling the item has been encountered before, but the context in which it was encountered is not retrieved.[5] According to this view, remember responses reflect recollections of past experiences and know responses are associated with recognition on the basis of familiarity.[7] Signal-detection theory
According to this theory, recognition decisions are based on the strength of a memory trace in reference to a certain decision threshold. A memory that exceeds this threshold is perceived as old, and trace that does not exceed the threshold is perceived as new. According to this theory, remember and know responses are products of different degrees of memory strength. There are two criteria on a decision axis; a point low on the axis is associated with a know decision, and a point high on the axis is associated with a remember decision.[5] If memory strength is high, individuals make a “remember” response, and if memory strength is low, individuals make a “know” response.[5]
Probably the strongest support for the use of signal detection theory in recognition memory came from the analysis of ROCs. An ROC is the function that relates the proportion of correct recognitions (hit rate) to the proportion of incorrect recognitions (false-alarm rate).[8]
Signal-detection theory assumed a preeminent position in the field of recognition memory in large part because its predictions about the shape of the ROC were almost always shown to be more accurate than the predictions of the intuitively plausible high-threshold model. [5] More specifically, the signal-detection model, which assumes that memory strength is a graded phenomenon (not a discrete, probabilistic phenomenon) predicts that the ROC will be curvilinear, and because every recognition memory ROC analyzed between 1958 and 1997 was curvilinear, the high-threshold model was abandoned in favor of signal-detection theory.[5] Although signal-detection theory predicts a curvilinear ROC when the hit rate is plotted against the false alarm rate, it predicts a linear ROC when the hit and false alarm rates are converted to z scores (yielding a z-ROC).[5]
“The predictive power of the signal detection modem seems to rely on know responses being related to transient feelings of familiarity without conscious recollection, rather than Tulving’s (1985) original definition of know awareness. [9] Dual-process signal-detection/high-threshold theory
The dual-process signal-detection/high-threshold theory tries to reconcile dual-process theory and signal-detection theory into one main theory. This theory states that recollection is governed by a threshold process, while familiarity is not.[5] Recollection is a high-threshold process (i.e., recollection either occurs or does not occur), whereas familiarity is a continuous variable that is governed by an equal-variance detection model.[5] On a recognition test, item recognition is based on recollection if the target item has exceeded threshold, producing an “old” response.[5] If the target item does not reach threshold, the individual must make an item recognition decision based on familiarity.[5] According to this theory, an individual makes a “remember” response when recollection has occurred. A know response is made when recollection has not occurred, and the individual must decide whether they recognize the target item solely on familiarity.[5] Thus, in this model, the participant is thought to resort to familiarity as a backup process whenever recollection fails to occur.[5] Distinctiveness/fluency model
In the past, it was suggested that remembering is associated with conceptual processing and knowing is associated with perceptual processing. However, recent studies have reported that there are some conceptual factors that influence knowing and some perceptual factors that influence remembering.[2] Findings suggest that regardless of perceptual or conceptual factors, distinctiveness of processing at encoding is what affects remembering, and fluency of processing is what affects knowing.[2] Remembering is associated with distinctiveness because it is seen as an effortful, consciously controlled process.[2] Knowing, on the other hand, depends on fluency as it is more automatic and reflexic and requires much less effort.[2]”″