A condensed version of this has been published as Can we do better than ACH? AIPIO News, Issue 55, December 2008, pp.4-5.

The “Analysis of Competing Hypotheses” method, or ACH, is one of the most important tools on the intelligence analyst’s bench. It is a procedure for determining which of a range of hypotheses is most likely to be true, given the available evidence. At its heart is a matrix, wherein hypotheses are listed across the top, and items of evidence are listed down the left side. There is then a square or cell in the matrix corresponding to every hypothesis/evidence pair, and in that square one indicates whether the item of evidence is (in)consistent or neutral with the hypothesis. For more information on ACH, see

  • the classic chapter by Richards Heuer
  • This brief overview (pdf file) of ACH compared with argument mapping (AM). Some of the points made below are presaged in the overview.

ACH is based on some fundamental insights:

  • The network of relationships between items of evidence and hypothesis is “many-many”. That is, one piece of evidence can bear, one way or another, on many hypotheses, and an hypothesis is generally considered in the light of a number of pieces of evidence. The ACH matrix is an obvious and natural way to accommodate this web of relationships.
  • At least in many situations, structured thinking techniques yield better results than informal or intuitive “pondering”. The ACH imposes a strong structure on hypothesis testing.
  • Structured techniques are even more effective when making use of suitable external (i.e., outside the head or “on paper) representations. Thus long division in the head is hard; on paper, following a standard procedure, it is easy. The ACH matrix is an external representation aiding hypothesis testing.
  • When making informal or qualitative judgements, it is usually better to use coarse schemes such as consistent/neutral/inconsistent rather than more elaborate and precise schemes such as numerical consistency ratings.

Nevertheless, in my experience using ACH, difficulties of various sorts rapidly arise; and as the expenditures of mental effort involved in struggling with those difficulties mount up, alternatives, such as “muddling through” without the use of a tool such as ACH, or using some other tool such as argument mapping, look increasingly attractive.

(Admittedly, I’ve never tried using ACH on a real, “industrial strength” problem of the kind that, presumably, intelligence analysts are engaging with on a daily or at least weekly basis. Perhaps the difficulties don’t arise so much in real cases; or perhaps they do arise, but are more than compensated for by the various benefits of using the ACH method, given the complexity of real cases. Perhaps; but I doubt it.)

Further, I’ve heard that while some intelligence analysts use the ACH technique regularly and perhaps even enthusiastically, the majority tend not to use it unless they really have to. It seems that their perception is that ACH is not worth the effort. Presumably this can be explained in part in terms of the various difficulties discussed here.

1. Too many judgements to make.

ACH, at least in a strong form, requires that you enter a judgement of consistency for every evidence item/hypothesis pair; i.e., you have to fill in every cell in the matrix. This is both a great strength of ACH, and a serious problem. It is a strength because it makes the process of comparing hypotheses against evidence exhaustive, thereby helping ensure that the evidential weight of all the items of evidence is properly accounted for.

The trouble is that the number of separate judgements becomes very large; for example, with 20 items of evidence and 5 hypotheses, you’d have to make 100 distinct judgements, each taking some modicum of conscious mental effort. Ugh! To make matters worse, many of these judgements return a “nil” verdict. In other words, in many cases, after careful consideration you conclude that item of evidence e is neutral (“neither here nor there”) with respect to hypothesis h.

So for example, suppose you are investigating the death of Princess Diana, and you are considering hypotheses including drunk-driving accident and assassination by MI5; and that one piece of evidence is that the driver had been drinking prior to the crash. This is clearly consistent with the drunk-driving hypothesis. ACH requires you to also consider whether this item of evidence is consistent, neutral or inconsistent with the assassination hypothesis. So you consider it, and you conclude that it is neutral; it really has nothing to do with that hypothesis.

In such a case, the mental effort of making the judgement seems to have yielded no immediate progress towards the goal of assessing the relative merits of the hypotheses. Arguably, that effort has in fact yielded some value in the context of the overall process, value which becomes apparent when you look across a row (to assess diagnosticity of evidence) or down a column (to assess the plausibility of an hypothesis). But it takes serious commitment to crank through dozens of such boring judgements in pursuit of some result at the end of the process. When in the midst of the ACH procedure, being forced to consider every e in relation to every h, only to conclude that it is (in and of itself) irrelevant, is a dispiriting activity; it feels like “makework” demanded arbitrarily by a tedious and laborious process.

(2) No e is an island

Superficially, ACH treats an item of evidence as consistent or inconsistent on its own with each of the hypotheses. Thus it seems to make sense to ask whether [the driver’s drinking before the crash] is consistent with the hypothesis that [the death of Diana was a drunk-driving accident]. However this is an illusion. In fact, and always, the evidential relationship between one proposition and another is mediated by other propositions. Put another way, an item of evidence is only consistent or otherwise with an hypothesis in the context of other relevant pieces of information or assertions. Thus the drink driver’s drinking before the crash is only consistent with the drunk-driving accident hypothesis given the general background knowledge that driving under the influence of alcohol increases the chances of an accident. If this were false – if drinking improved driving – then the driver’s drinking would be inconsistent with the drunk-driving hypothesis.

In argument mapping terms, we would say that every reason or objection is actually a multi-premise structure. In the philosophy of science, we would say that observations only confirm or disconfirm hypotheses in the context of auxiliary hypotheses. Sometimes we call these additional propositions assumptions. However we cast the point, the fundamental problem is that ACH’s way of structuring the evidence, hypotheses and their relationships leaves something important out of the picture. The kernel of the problem is the matrix representation at the heart of ACH; it naturally pairs individual items of evidence with individual hypotheses, and so is ill-suited to handling the actual structure of evidential relations even in the simplest case.

Does this matter? By necessity, every graphical or structural display of the web of evidential relations must select and simplify. The question is whether a particular display is, on balance, useful. Does the display enable us to think through the issues more effectively than using our default, informal and “in the head” methods? ACH enthusiasts of course think that the tradeoff is a good one. However, I think that while choosing a way to organise evidence and hypotheses which treats items of evidence discretely and independently of other information offers short-term gains, it does so at the cost of problems further down the track.

One such situation is where an additional item of information comes in, which has the effect of undermining a co-premise/auxiliary hypothesis/assumption. To illustrate: consider the question of what caused the Permian Extinction. One hypothesis is

h: it was a massive meteor collision.

A relevant piece of evidence is that

e1: there is no known meteor impact crater of the right age.

This appears to be inconsistent with the meteor hypothesis. Later, you find out that

e2: it is possible for lava to flow back up through the hole created in a large meteor impact, erasing the impact crater.

Now, the question is, how to accommodate this new piece of information in an ACH matrix? It seems to make little sense to treat it as a new, independent piece of evidence, against which each hypothesis can be tested. So the only option left is to leave it out of the matrix, but to change the “inconsistent” rating of e1 wrt h to neutral or consistent. However without e2, such a rating is mysterious. It seems e2 has to be recorded somewhere, but the ACH matrix offers no space for it.

A better treatment of this situation is to recognise that e1 is inconsistent with h only given the natural assumption that

a: A large meteor impact would leave a crater.

e1 alone is not inconsistent with h; rather, it is the bundle [e1, a] which is inconsistent with h; or alternatively, e1 is inconsistent with [h given a]. e2 is then a challenge to a.

However we express this verbally, the fundamental problem is that you can’t adequately represent, and make sense of, what is going on here in a basic ACH format. (You can handle this sort of situation quite easily in an argument mapping format, but that is another topic.)

(3) Flat structure of hypotheses

Another major problem with ACH is that it cannot handle the hierarchical structure of hypotheses (or it can do so at best only in an ungainly and unilluminating manner).

Hypotheses can be more or less general or abstract, and a general hypothesis can have sub-hypotheses. So in the Princess Diana case, one general hypothesis is assassination and another general one is accident. The general assassination hypothesis can have sub-hypotheses such as assassination by MI5, assassination by mafia, etc..

This is important because distinct items of evidence can count for or against hypotheses at various levels. Thus a bullet hole in the limousine would count in favour of any assassination hypothesis (or at least many such hypotheses), while an internal MI5 document might count for or against only the MI5 sub-hypothesis.

The classic ACH matrix asks for all hypotheses to be entered individually across the top row, and then to be compared against all pieces of evidence. But in the case of an hierarchical structure of hypotheses, this will result in an absurd duplication of effort, in which for example a piece of evidence bearing on all assassination hypotheses is compared not only against the general assassination hypothesis but also against all its sub-cases.

(4) Subordinate deliberation

By its very nature, being based on a matrix structure, the ACH approach does not consider what is “behind” or “underneath” any given piece of evidence. From a piece of evidence, it looks “forwards” or “upwards” to its bearing on the hypotheses under consideration. However the weight of a piece of evidence wrt an hypothesis depends on information bearing upon that piece of evidence. e may be quite (in)consistent with h, but how seriously we take this (in)consistency depends on how seriously we take e itself (its plausibility or credibility). This can only be evaluated in the light of further information subordinate to e. If you like, think of e as itself an hypothesis, in relation to which there is supporting or opposing evidence. In the standard ACH framework there is no way to represent or display this layered structure. (Again, the ability to handle such structure is a strength of argument mapping.)

(5) Decontextualisation and discombobulation

We’ve seen in points 2 and 4 above that the ACH matrix does not accommodate co-premises/assumptions, or subordinate deliberation. An ACH matrix is a like a sieve on the web of evidence, letting through some items and relationships but keeping out many others. Unfortunately what is left out is the context which helps make sense of the relationship of any given item of evidence to an hypothesis. Absent that context, the judgement becomes difficult to make. For a not-very-exaggerated example, consider: Is

e: David Hicks was captured in Afghanistan

consistent, inconsistent, or neutral, with respect to:

h: David Hicks was a terrorist

The proper answer is: uh….dunno…it depends. Absent any other information, you’d probably choose neutral, but this is not because e is neutral wrt to h. It is only because without surrounding information it is hard to tell what the evidential value of e is.

ACH, in demanding that we make so many judgements even as it strips the context of those judgements away, is constantly asking us to engage in these sorts of mentally taxing, even discombobulating exercises. After an extended bout of ACH, I tend to feel a bit dazed and confused, and have to stave off that feeling with redoubled mental effort to see the sense of the judgements I’m making.


We might reduce my complaints about ACH to two:

  1. ACH asks us to make too many distinct judgements; and
  2. Those judgements are emaciated due to the stripping away of relevant context, of both hypotheses and evidence

These problems are deeply related to choice of structure of external representation, i.e., to the choice of a matrix as the way to organise evidence, hypotheses, and judgements. I’m inclined to think that the use of the matrix is the fatal mistake of ACH; it is a commitment which seems obvious and natural initially, but as things unfold the limitations and problems inherent in the matrix structure come to the fore.

Much of the ACH procedure, as outlined for example by Heuer, could be retained even if the matrix structure was dispensed with in favour of some richer, more flexible format. But if you throw out the matrix, you also must throw out all those further aspects of the classic ACH which only applied if a matrix was being used. It is doubtful that what you’d have left would be worth calling ACH.

If you wanted to replace the ACH matrix, what would you use? One candidate is the argument map (of the kind you can create in, for example, the Rationale software). However while these have some strengths, for hypothesis testing they have a complementary set of weaknesses. At Austhink we are working on a new structure, one which will take and blend the best elements of both ACH and argument mapping, thus superseding them both. This new structure enables users to rapidly and intuitively assemble a (hierarchical) set of hypotheses in relation to some issue, items of evidence bearing on multiple hypotheses, assumptions, subordinate considerations, etc..