Delphi and group estimation

A software estimate is a prediction about the future. Software developers were not the first people to formalize processes for making predictions about the future. Starting in the last 1940s, the RAND Corporation’s Delphi project created what became known as the Delphi method, e.g., An Experiment in Estimation, and Construction of Group Preference Relations by Iteration.

In its original form experts were anonymous; there was a “… deliberate attempt to avoid the disadvantages associated with more conventional uses of experts, such as round-table discussions or other milder forms of confrontation with opposing views.”, and no rules were given for the number of iterations. The questions involved issues whose answers involved long term planning, e.g., how many nuclear weapons did the Soviet Union possess (this study asked five questions, which required five estimates). Experts could provide multiple answers, and had to give a probability for each being true.

One of those involved in the Delphi project (Helmer-Hirschberg) co-founded the Institute for the Future, which published reports about the future based on answers obtained using the Delphi method, e.g., a 1970 prediction of the state-of-the-art of computer development by the year 2000 (Dalkey, a productive member of the project, stayed at RAND).

The first application of Delphi to software estimation was by Farquhar in 1970 (no pdf available), and Boehm is said to have modified the Delphi process to have the ‘experts’ meet together, rather than be anonymous, (I don’t have a copy of Farquhar, and my copy of Boehm’s book is in a box I cannot easily get to); this meeting together form of Delphi is known as Wideband Delphi.

Planning poker is a variant of Wideband Delphi.

An assessment of Delphi by Sackman (of Grant-Sackman fame) found that: “Much of the popularity and acceptance of Delphi rests on the claim of the superiority of group over individual opinions, and the preferability of private opinion over face-to-face confrontation.” The Oracle at Delphi was one person, have we learned something new since that time?

Group dynamics is covered in section 3.4 of my Evidence-based software engineering book; resource estimation is covered in section 5.3.

The likelihood that a group will outperform an individual has been found to depend on the kind of problem. Is software estimation the kind of problem where a group is likely to outperform an individual? Obviously it will depend on the expertise of those in the group, relative to what is being estimated.

What does the evidence have to say about the accuracy of the Delphi method and its spinoffs?

When asked to come up with a list of issues associated with solving a problem, groups generate longer lists of issues than individuals. The average number of issues per person is smaller, but efficient use of people is not the topic here. Having a more complete list of issues ought to be good for accurate estimating (the validity of the issues is dependent on the expertise of those involved).

There are patterns of consistent variability in the estimates made by individuals; some people tend to consistently over-estimate, while others consistently under-estimate. A group will probably contain a mixture of people who tend to over/under estimate, and an iterative estimation process that leads to convergence is likely to produce a middling result.

By how much do some people under/over estimate?

The multiplicative factor values (y-axis) appearing in the plot below are from a regression model fitted to estimate/actual implementation time for a project involving 13,669 tasks and 47 developers (data from a study Nichols, McHale, Sweeney, Snavely and Volkmann). Each vertical line, or single red plus, is one person (at least four estimates needed to be made for a red plus to occur); the red pluses are the regression model’s multiplicative factor for that person’s estimates of a particular kind of creation task, e.g., design, coding, or testing. Points below the grey line are overestimation, and above the grey line the underestimation (code+data):

3n+1 programs containing various lines of code.

What is the probability of a Delphi estimate being more accurate than an individual’s estimate?

If we assume that a middling answer is more likely to be correct, then we need to calculate the probability that the mix of people in a Delphi group produces a middling estimate while the individual produces a more extreme estimate.

I don’t have any Wideband Delphi estimation data (or rather, I only have tiny amounts); pointers to such data are most welcome.

The wisdom of the ancients

The software engineering ancients are people like Halstead and McCabe, along with less well known ancients (because they don’t name anything after them) such as Boehm for cost estimation, Lehman for software evolution, and Brooks because of a book; these ancients date from before 1980.

Why is the wisdom of these ancients still venerated (i.e., people treat them as being true), despite the evidence that they are very inaccurate (apart from Brooks)?

People hate a belief vacuum, they want to believe things.

The correlation between Halstead’s and McCabe’s metrics, and various software characteristics is no better than counting lines of code, but using a fancy formula feels more sophisticated and everybody else uses them, and we don’t have anything more accurate.

That last point is the killer, in many (most?) cases we don’t have any metrics that perform better than counting lines of code (other than taking the log of the number of lines of code).

Something similar happened in astronomy. Placing the Earth at the center of the solar system results in inaccurate predictions of where the planets are going to be in the sky; adding epicycles to the model helps to reduce the error. Until Newton came along with a model that produced very accurate results, people stuck with what they knew.

The continued visibility of COCOMO is a good example of how academic advertising (i.e., publishing papers) can keep an idea alive. Despite being more sophisticated, the Putnam model is not nearly as well known; Putnam formed a consulting company to promote this model, and so advertised to a different market.

Both COCOMO and Putnam have lines of code as an integral component of their models, and there is huge variability in the number of lines written by different people to implement the same functionality.

People tend not to talk about Lehman’s quantitative work on software evolution (tiny data set, and the fitted equation is very different from what is seen today). However, Lehman stated enough laws, and changed them often enough, that it’s possible to find something in there that relates to today’s view of software evolution.

Brooks’ book “The Mythical Man-Month” deals with project progress and manpower; what he says is timeless. The problem is that while lots of people seem happy to cite him, very few people seem to have read the book (which is a shame).

There is a book coming out this year that provides lots of evidence that the ancient wisdom is wrong or at best harmless, but it does not contain more accurate models to replace what currently exists :-(

Moving to the 12th circle in fault prediction modeling

Most software fault prediction papers are based on a false assumption, i.e., a list of dates when a fault was first experienced, by a program, contains enough information to build a model that has a connection to reality. A count of faults that have been experienced twice is required to fit a basic model that has some mathematical connection to reality.

I had thought that people had moved on from writing papers that fitted yet more complicated equations to one of the regularly used data sets. No, it seems they have just switched to publishing someplace they have not been seen before.

Table 1 lists the every increasing number of circles within circles; the new model is proposed as the 12th refinement (the table is a summary, lots of forks have been proposed over the years). I have this sinking feeling there is another paper in the works, one that ‘benchmarks’ the new equation using a collection of the other regular characters data sets that appear in papers of this kind.

Fitting an equation to data of first experience of a fault is little better than fitting noise.

As Planck famously said, science advances one funeral at a time.

Estimating the number of distinct faults in a program

In an earlier post I gave two reasons why most fault prediction research is a waste of time: 1) it ignores the usage (e.g., more heavily used software is likely to have more reported faults than rarely used software), and 2) the data in public bug repositories contains lots of noise (i.e., lots of cleaning needs to be done before any reliable analysis can done).

Around a year ago I found out about a third reason why most estimates of number of faults remaining are nonsense; not enough signal in the data. Date/time of first discovery of a distinct fault does not contain enough information to distinguish between possible exponential order models (technical details; practically all models are derived from the exponential family of probability distributions); controlling for usage and cleaning the data is not enough. Having spent a lot of time, over the years, collecting exactly this kind of information, I was very annoyed.

The information required, to have any chance of making a reliable prediction about the likely total number of distinct faults, is a count of all fault experiences, i.e., multiple instances of the same fault need to be recorded.

The correct techniques to use are based on work that dates back to Turing’s work breaking the Enigma codes; people have probably heard of Good-Turing smoothing, but the slightly later work of Good and Toulmin is applicable here. The person whose name appears on nearly all the major (and many minor) papers on population estimation theory (in ecology) is Anne Chao.

The Chao1 model (as it is generally known) is based on a count of the number of distinct faults that occur once and twice (the Chao2 model applies when presence/absence information is available from independent sites, e.g., individuals reporting problems during a code review). The estimated lower bound on the number of distinct items in a closed population is:

S_{est} ge S_{obs}+{n-1}/{n}{f^2_1}/{2f_2}

and its standard deviation is:

S_{sd-est}=sqrt{f_2 [0.25k^2 ({f_1}/{f_2} )^4+k^2 ({f_1}/{f_2} )^3+0.5k ({f_1}/{f_2} )^2 ]}

where: S_{est} is the estimated number of distinct faults, S_{obs} the observed number of distinct faults, n the total number of faults, f_1 the number of distinct faults that occurred once, f_2 the number of distinct faults that occurred twice, k={n-1}/{n}.

A later improved model, known as iChoa1, includes counts of distinct faults occurring three and four times.

Where can clean fault experience data, where the number of inputs have been controlled, be obtained? Fuzzing has become very popular during the last few years and many of the people doing this work have kept detailed data that is sometimes available for download (other times an email is required).

Kaminsky, Cecchetti and Eddington ran a very interesting fuzzing study, where they fuzzed three versions of Microsoft Office (plus various Open Source tools) and made their data available.

The faults of interest in this study were those that caused the program to crash. The plot below (code+data) shows the expected growth in the number of previously unseen faults in Microsoft Office 2003, 2007 and 2010, along with 95% confidence intervals; the x-axis is the number of faults experienced, the y-axis the number of distinct faults.

Predicted growth of unique faults experienced in Microsoft Office

The take-away point: if you are analyzing reported faults, the information needed to build models is contained in the number of times each distinct fault occurred.