Some human biases in conditional reasoning

Tracking down coding mistakes is a common developer activity (for which training is rarely provided).

Debugging code involves reasoning about differences between the actual and expected output produced by particular program input. The goal is to figure out the coding mistake, or at least narrow down the portion of code likely to contain the mistake.

Interest in human reasoning dates back to at least ancient Greece, e.g., Aristotle and his syllogisms. The study of the psychology of reasoning is very recent; the field was essentially kick-started in 1966 by the surprising results of the Wason selection task.

Debugging involves a form of deductive reasoning known as conditional reasoning. The simplest form of conditional reasoning involves an input that can take one of two states, along with an output that can take one of two states. Using coding notation, this might be written as:

    if (p) then q       if (p) then !q
    if (!p) then q      if (!p) then !q

The notation used by the researchers who run these studies is a 2×2 contingency table (or conditional matrix):

          OUTPUT
          1    0
   
      1   A    B
INPUT
      0   C    D

where: A, B, C, and D are the number of occurrences of each case; in code notation, p is the input and q the output.

The fertilizer-plant problem is an example of the kind of scenario subjects answer questions about in studies. Subjects are told that a horticultural laboratory is testing the effectiveness of 31 fertilizers on the flowering of plants; they are told the number of plants that flowered when given fertilizer (A), the number that did not flower when given fertilizer (B), the number that flowered when not given fertilizer (C), and the number that did not flower when not given any fertilizer (D). They are then asked to evaluate the effectiveness of the fertilizer on plant flowering. After the experiment, subjects are asked about any strategies they used to make judgments.

Needless to say, subjects do not make use of the available information in a way that researchers consider to be optimal, e.g., Allan’s Delta p index Delta p=P(A vert C)-P(B vert D)=A/{A+B}-C/{C+D} (sorry about the double, vert, rather than single, vertical lines).

What do we know after 40+ years of active research into this basic form of conditional reasoning?

The results consistently find, for this and other problems, that the information A is given more weight than B, which is given by weight than C, which is given more weight than D.

That information provided by A and B is given more weight than C and D is an example of a positive test strategy, a well-known human characteristic.

Various models have been proposed to ‘explain’ the relative ordering of information weighting: w(A)>w(B) > w(C) > w(D)” title=”w(A)>w(B) > w(C) > w(D)”/><a href=, e.g., that subjects have a bias towards sufficiency information compared to necessary information.

Subjects do not always analyse separate contingency tables in isolation. The term blocking is given to the situation where the predictive strength of one input is influenced by the predictive strength of another input (this process is sometimes known as the cue competition effect). Debugging is an evolutionary process, often involving multiple test inputs. I’m sure readers will be familiar with the situation where the output behavior from one input motivates a misinterpretation of the behaviour produced by a different input.

The use of logical inference is a commonly used approach to the debugging process (my suggestions that a statistical approach may at times be more effective tend to attract odd looks). Early studies of contingency reasoning were dominated by statistical models, with inferential models appearing later.

Debugging also involves causal reasoning, i.e., searching for the coding mistake that is causing the current output to be different from that expected. False beliefs about causal relationships can be a huge waste of developer time, and research on the illusion of causality investigates, among other things, how human interpretation of the information contained in contingency tables can be ‘de-biased’.

The apparently simple problem of human conditional reasoning over two variables, each having two states, has proven to be a surprisingly difficult to model. It is tempting to think that the performance of professional software developers would be closer to the ideal, compared to the typical experimental subject (e.g., psychology undergraduates or Mturk workers), but I’m not sure whether I would put money on it.

The impact of believability on reasoning performance

What are the processes involved in reasoning? While philosophers have been thinking about this question for several thousand years, psychologists have been running human reasoning experiments for less than a hundred years (things took off in the late 1960s with the Wason selection task).

Reasoning is a crucial ability for software developers, and I thought that there would be lots to learn from the cognitive psychologists research into reasoning. After buying all the books, and reading lots of papers, I realised that the subject was mostly convoluted rabbit holes individually constructed by tiny groups of researchers. The field of decision-making is where those psychologists interested in reasoning, and a connection to reality, hang-out.

Is there anything that can be learned from research into human reasoning (other than that different people appear to use different techniques, and some problems are more likely to involve particular techniques)?

A consistent result from experiments involving syllogistic reasoning is that subjects are more likely to agree that a conclusion they find believable follows from the premise (and are more likely to disagree with a conclusion they find unbelievable). The following is perhaps the most famous syllogism (the first two lines are known as the premise, and the last line is the conclusion):

    All men are mortal.
    Socrates is a man.
    Therefore, Socrates is mortal. 

Would anybody other than a classically trained scholar consider that a form of logic invented by Aristotle provides a reasonable basis for evaluating reasoning performance?

Given the importance of reasoning ability in software development, there ought to be some selection pressure on those who regularly write software, e.g., software developers ought to give a higher percentage of correct answers to reasoning problems than the general population. If the selection pressure for reasoning ability is not that great, at least software developers have had a lot more experience solving this kind of problem, and practice should improve performance.

The subjects in most psychology experiments are psychology undergraduates studying in the department of the researcher running the experiment, i.e., not the general population. Psychology is a numerate discipline, or at least the components I have read up on have a numeric orientation, and I have met a fair few psychology researchers who are decent programmers. Psychology undergraduates must have an above general-population performance on syllogism problems, but better than professional developers? I don’t think so, but then I may be biased.

A study by Winiger, Singmann, and Kellen asked subjects to specify whether the conclusion of a syllogism was valid/invalid/don’t know. The syllogisms used were some combination of valid/invalid and believable/unbelievable; examples below:

        Believable                  Unbelievable
Valid
        No oaks are jubs.           No trees are punds.
        Some trees are jubs.        Some Oaks are punds.
        Therefore, some trees       Therefore, some oaks
                   are not oaks.               are not trees.
Invalid
        No tree are brops.          No oaks are foins.
        Some oaks are brops.        Some trees are foins.
        Therefore, some trees       Therefore, some oaks
                   are not oaks.               are not trees.

The experiment was run using an online crowdsource site, and 354 data sets were obtained.

The plot below shows the impact of conclusion believability (red)/unbelievability (blue/green) on subject performance, when deciding whether a syllogism was valid (left) or invalid (right), (code+data):

Benchmark runtime at various array sizes, for each algorithm using a 32-bit datatype.

The believability of the conclusion biases the responses away/towards the correct answer (the error bars are tiny, and have not been plotted). Building a regression model puts numbers to the difference, and information on the kind of premise can also be included in the model.

Do professional developers exhibit such a large response bias (I would expect their average performance to be better)?

People tend to write fewer negative tests, than positive tests. Is this behavior related to the believability that certain negative events can occur?

Believability is an underappreciated coding issue.

Hopefully people will start doing experiments to investigate this issue :-)