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Implementación de las ecuaciones de salida del canal en Matlab

CAPÍTULO 3. “COMPARACIÓN E IMPLEMENTACIÓN DE LOS ALGORITMOS

3.2 Herramientas de simulación para la implementación matemática de algoritmos

3.2.2 Implementación de las ecuaciones de salida del canal en Matlab

Having identified some key challenges faced by much of the research on confirmation

bias, we can take a more systematic look at how each of the findings discussed fare against these challenges. We pass each of the findings discussed through three stages of

scrutiny:

1. How robust is the finding? That is, does the tendency that is claimed to exist even clearly exist - before even we ask whether it’s evidence of a confirmation bias?

2. Does the finding show asystematic tendency to confirm the focal hypothesis?

3. Is the finding said to be irrational relative to some explicitnormative standard? How much agreement is there that this is the appropriate normative standard?

Table 2.6: How strong is each piece of evidence for confirmation bias?

Finding Robust? Confirmatory? Non-normative? Bias in search

Bias in hypothesis testing: particularly the use of positive test strategies, asking questions expected to yield positive answers if the hypothesis is correct (Snyder and Swann, 1978, Wason, 1960, 1968)

Not very - positive test strategy seems robust in Wasons basic paradigm, but less clear when extended to more familiar contexts (where people seem more likely to ask diagnostic questions)

Not necessarily - a positive test strategy can sometimes lead to disconfirmation (by identifying false positives), so isnt the same as confirmatory reasoning.

Contested - some have argued that

falsification is not the appropriate normative standard for

hypothesis testing (Oaksford and Chater, 1994), and that a positive test strategy may be accurate across most real-life scenarios. Selective exposure: looking for information in places expected to support current hypothesis (Hart et al., 2009) No - several decades of research have

produced very mixed findings, with some studies finding the opposite effect, and effects seeming highly dependent on subtle moderating factors. Not necessarily - whether or not selective exposure leads to confirmation depends largely on how information is interpreted, and the motivations/intentions behind seeking out different types of info.

No - there are no explicit normative standards in selective exposure studies, and it is simply assumed that unbiased means reading equal arguments on either side of an issue. Myside bias in argument production: selectively searching memory for confirmatory info (Toplak and Stanovich, 2003) Fairly robust - no contrary findings, but we did not find particularly thorough or extensive research on this tendency. Not necessarily.

There is some evidence that people tend to find it easier to produce one-sided arguments, even if the side they are being asked to argue for is not their own position - suggesting that the tendency is not so much to confirm ones existing beliefs, but a difficulty splitting attention between two sides of an issue.

No explicit normative standards are used, and its acknowledged (e.g. by Wolfe and Britt (2008) that this tendency is not necessarily a bias - whether or not it is considered one depends on what people believe the goal/purpose of generating arguments is.

Finding Robust? Confirmatory? Non-normative? Bias in amount of

time spent searching: stopping search for information when evidence points in favour of

current/favoured hypothesis, continuing search for information when it does not (Ditto and Lopez, 1992)

Not very - most of the evidence for this tendency comes from studies of motivated reasoning, not confirmation bias per se.

Not necessarily - since much of the evidence here comes from the motivated reasoning literature, it may be that people terminate information search depending on whether they have reached a conclusion they like - which is not

necessarily the same as confirming their current belief.

No - the way bias is generally measured in these studies is somewhat intuitive, but this intuition is not justified any further. Bias in inference Interpreting ambiguous evidence as supportiveof currently favoured hypothesis (Feeney et al., 2000, Fischoff and Beyth-Marom, 1983)

Unclear - much of the evidence commonly cited for this tendency is actually evidence for the related but subtly different tendency of pseudodiagnosticity - seeking diagnostically useless information. Evidence that people actually interpret evidence as more diagnostic than it should be is less clear.

Probably, but not always - if such a tendency did exist, it would seem likely to result in a tendency to confirm the focal hypothesis. This is not totally a given, however - as Klayman (1995) points out, this does also require that people do not anticipate and adjust for this tendency in how they search for information.

Not necessarily - the normative standards for assessing the diagnosticity of evidence are clearer than those used in many studies, but it has been challenged whether or not maximising diagnosticity is the best norm for choosing what information to sample (Nelson, 2005).

Finding Robust? Confirmatory? Non-normative? Applying different standards of scrutiny/evaluation to supporting and conflicting evidence - biased assimilation and polarization (Lord et al., 1979, Pyszczynski and Greenberg, 1987, Taber and Lodge, 2006)

Fairly - since Lord et al. (1979), several other studies have found similar results - that people with differing prior beliefs interpret the same information differently and therefore diverge in their resultant opinions. However, there have also been some failed replication attempts (Kuhn and Lao, 1996).

Yes. Not necessarily - studies of biased assimilation generally do not use explicit normative standards, instead assuming that it must be irrational for people to draw different conclusions from the same information. However, Jern et al. (2014) point out that this can be rational, if people genuinely have different prior information that influences their interpretation of information - and use more explicit normative models to show how this can occur.

Finding Robust? Confirmatory? Non-normative? Belief persistencein

the debriefing paradigm (Ross et al., 1975)

Yes, fairly - the main effect has been replicated across a range of scenarios.

Yes, basically by definition - persisting in the current belief is a form of confirmation - however, whether belief persistence actually results from specific confirmatory reasoning processes (e.g. biased assimilation), is less clear.

No, not necessarily - studies of belief persistence generally do not invoke any explicit normative standards (other than the intuitive people should not persist in believing things when the evidence is discredited.) This fails to account for the possibility that people may have subsequently found or remembered additional evidence for their belief, or that they may not entirely trust the retraction of evidence, for example.

Persistence of misinformationin society despite corrections (Lewandowsky et al., 2012)

Fairly robust - this has been observed in public opinion for a range of topics (Lewandowsky et al., 2012), and in some more controlled contexts (Nyhan and Reifler, 2010)

Yes, with the same caveat as belief persistence above (its not clear exactly what kinds of processes lead to persistence.)

No, not necessarily. Particularly when looking at public opinion in naturalistic contexts, it is very difficult to draw normative conclusions about what people should believe, without knowing what information they have access to. In a narrow sense we can say that believing false things is non-normative, of course. But we cannot necessarily say that people are irrational to believe these things.

Finding Robust? Confirmatory? Non-normative? Conservatism bias:

updating beliefs conservatively with respect to Bayes rule (Edwards, 1982)

Fairly robust - shown across multiple experiments in a highly controlled paradigm.

No, not necessarily - the finding is that participants update conservatively on all evidence, no matter which direction it points in. Not necessarily - Corner et al. (2010) argue that

conservatism bias may be an experimental artefact resulting from the fact that

participants do not entirely trust the evidence given to them, rather than demonstrating irrationality.

Overconfidence: holding beliefs more strongly or with more precision than is rational (Moore et al., 2015)

Fairly robust - the overprecision form of overconfidence seems more robust than other types, but has also been less studied, so is harder to draw very strong conclusions about. Again, by definition overconfidence is a kind of confirmatory reasoning - but its also unclear whether overconfidence is necessarily the result of certain confirmatory reasoning processes or not (since

overconfidence has generally been studied independently of the processes leading to it.)

Not necessarily - saying how strong peoples beliefs should be requires using very specific experimental paradigms where normative standards are made explicit. A problem here is that this often means it is difficult to assess whether people are overconfident about the kinds of things we are typically most interested in (political beliefs say, as opposed to numerical estimates of quantities.)

Going through each of the tendencies we’ve discussed in this systematic way in table

2.6, we can see much more clearly just how tenuous the case for confirmation bias is. None of the findings discussed pass all three hurdles - demonstrating a robust tendency,

that actually leads to confirmatory reasoning, and which can be shown to fall short of a clear normative standard. Perhaps those findings that fare best here are those related

to biased beliefs - findings of belief persistence and overconfidence seem to be the most robust of those we’ve covered. However, it’s not clear whether (a) these tendencies are

actually non-normative, particularly when it comes to issues where there is no ‘correct’ answer against which judgements can be compared, or whether (b) these tendencies are

actually the result of the kinds of biased processes generally referred to as ‘confirmation bias.’

The one dimension on which all of these findings fall short is the normative one - in every single case, normative standards are either not made explicit or have been contested for

one reason or another. These normative issues - around how people should reason, what it means to be rational, and what constitutes a bias - are much more complex than

they first seem, and I will discuss some of the disagreements that arise in more detail in chapter 4. For now, perhaps we might actually get a clearer picture of what is going

on if we set these complex normative issues aside, at least temporarily - stop asking how people should reason, and instead just ask what we know descriptively about how peopledo reason. For example, we might consider the following research conclusions in a more descriptive sense, independent of any claims of ‘confirmation bias’:

1. People do seem to often use a positive-test strategy in testing hypotheses, ask- ing questions for which the answer would be ‘yes’ if their current hypothesis is

true (Wason, 1960, 1968). This means people err towards holding overly-narrow hypotheses, and it is easier to identify false positives than false negatives.

2. People do not necessarily always seek out whatever information would be most

diagnostic, and often misjudge how diagnostic different pieces of information are, or are insufficiently sensitive to differences between diagnosticities of different pieces

of information (Slowiaczek et al., 1992).

3. There is some evidence that people have a weak preference for opinion-supportive

information in general (Hart et al., 2009), though this is highly dependent on and easily outweighed by other factors, such as how useful the information is for a

given task.

4. People do seem to have difficulty considering alternative hypotheses, and certainly considering multiple alternative hypotheses at once, unless explicitly instructed to

A few themes begin to arise here, and looking at these phenomena purely descriptively, we can ask why these tendencies might arise, what heuristics might underlie them. For

example, difficulty considering more than one hypothesis at once might explain quite a lot: why people tend to interpret information as more supportive of the focal hypothesis

than it in fact is (they only consider Pr(D | H) and not Pr(D | ¬H); an inclination to seek out more supportive information (such information will be more salient and

easier to search for); and more readily accepting supportive information (with only one hypothesis in mind, supportive information is easier to interpret and make sense of,

whereas information that conflicts with the focal hypothesis will take a lot more effort.)

It may also be true that people generally find it easier to reason with ‘positive’ informa-

tion than negative information. As well as a positive test strategy in hypothesis testing, there is also evidence that both people and animals find it easier to learn when learning

is based on the presence of features than their absence - supporting this idea that pos- itive and negative evidence are treated differently. Hearst and Wolff (1989) found that

pigeons learned twice as quickly when food would be available if this was indicated by thepresence of a light than by its absence, and Newman et al. (1980) find similar results for human learning.

Rather than continuing to focus on the general tendency of confirmation bias, research

might be better off focusing first instead on simply improving our descriptive picture of how people form and revise beliefs - what general principles and heuristics guide

the search for information, the testing of hypotheses, and the inferences people draw from information. If we’re able to get a clearer picture of how these processes work,

uncomplicated by terms like ‘bias’ and ‘rationality’, then perhaps we can begin to ask normative questions - looking at the costs and benefits of different tendencies in different

scenarios. This is not to suggest that it is not important and useful to ask normative questions; to ask where reasoning processes might perform better or worse - but that

it might be helpful to more clearly separate out descriptive and normative questions. This would help to clarify some complex normative issues and ensure that our descriptive