Section 31 Coding causal maps with propositions

Propositional maps differ from variable-based maps in many ways. Propositional maps encode answers to the question: what happened here and what caused it? Variable-based maps encode answers to the question: what causes what around here?

Here, I will discuss the most basic coding rule for bare-bones propositional causal maps, and discuss some extensions to it.

Even with the extensions, you still keep the core advantages of the propositional approach: you have propositions (and sets of propositions) causing other propositions. You are still dealing with historically true stories, not chatting about abstract models or what-might-happen-if. You still have something closer to an evaluation than to research.

[But: I argue that even the most basic causal coding anyway presupposes an understanding of an underlying causal claim behind the propositional claims, and that those causal claims always go beyond any specific piece of evidence. So it is not the case that “ooh, these extensions are risky, they go beyond the evidence to talk about abstract stuff”. Because the simplest propositional causal claim relies on background models of how things work.]

31.1 Basic coding rule

The basic coding unit is of the form “B causes E”.

B and E are both propositions. Both are true.

A proposition like B or E only has two possibilities; it is the case (which indeed it is), or it is not the case.

A proposition expresses a Difference. A good example of a Difference is a change, but other things can be Differences too (states, events, etc). It says that things are one way rather than some other, perhaps expected, contrast.

Examples

I bought a cow (as opposed to not buying one)
Yields have got worse (as opposed to not getting worse)
I am fairly happy (as opposed to not being fairly happy)
There is unemployment in the country at the moment (as opposed to there not being unemployment)

This also means that, seen like this, the items have no gradation. They are always one thing or the other. There are no possibilities in between. So “I am fairly happy” is not specifically contrasted with, say, “I am very happy”, but with any circumstances in which “I am fairly happy” is not true.

We have no way to code a proposition on its own; only as part of a causal statement.

We can be vague about the timing of things. The consequence has to come after the influence, or be concurrent in such a way that effects are still happening after causes.

31.1.1 Three claims

The basic coding rule encodes three claims:

the influence item is true
the consequence item is true
the first caused the second

This last claim is really important. We do not encode simple observations that things merely happen together. We are in fact encoding, in a minimal way, the causal knowledge of the respondent, a minimal part of her implicit causal map of the world. There is no way that merely observing B and E on their own warrants the causal conclusion.

The way that people tell stories usually implies beliefs that there are causal connections between the links of the story. We can usually assume that causal claims are being made. They don’t have to be made explicitly. “I got the cow. Now we have milk.”

31.1.2 The items have been witnessed

In general, the propositions are / have been personally true for, or at least personally experienced by the source or sources. We treat the source as a witness.

31.1.3 The propositions have contrastive implications

If someone makes a claim of the form that “X caused Y”, then this implies that if X had not happened in that way, Y wouldn’t have happened, and that if Y hadn’t happened, X can’t have happened. This is a strong claim: within this narrow context, holding everything else constant, X is necessary and sufficient for Y. Whenever X is true, Y is true, and vice versa.

This is quite another thing from saying that the people making it have to be in possession of corresponding statistical evidence, and is compatible with a proposition-based as well as a variable-based approach. Mosquito-bite claims are based on a more fundamental experience of causation than comparing a state of affairs with a counterfactual. But they do have counterfactual implications.

31.1.4 Can include claims about absence of expected states

I was expecting support from a safety net program but they excluded me from being a beneficiary so I am in financial difficulties

There is no reason not to code this kind of claim; the influence item is still a Difference, a difference from an expected state. It is no more or less hypothetical than any other causal claim.

31.2 Mini Extension: causal chains

Often we have to code narratives which take the form of chains. In this case, as the intervening item is one and the same proposition, we can join the two mini-maps into a causal chain. In practice we can do this as a single piece of coding.

This involves what I have elsewhere called the “chaining rule”. This also implies that we can deduce that as B causes C and C causes E, also B causes E. Of course this might seem naïve, of course other things explain my family’s health, but then all causal claims like this are naïve.

31.3 Mini Extensions: certainty and trust

There is no reason why we shouldn’t also encode additional attributes like the respondent’s degree of certainty:

I think the new irrigation methods improved my yields (this is the kind of thing which ought to work, and the results were encouraging) but I’m not really sure. [Coding: low certainty]

Or we can code the coder’s trust in the statement:

I saw a documentary and the state of the crops is definitely due to contrails. [Coding: low trust]

But as we have no way to even aggregate individual causal fragments, – no arithmetic for them – encoding certainty or trust amounts to no more than making a note alongside the fragment. They are not very interesting.

31.4 How does classic QuIP extend this basic idea?

That’s it. The result of one act of causal coding is just one mini-map, or a chain of them. The result of several acts of causal coding is a heap of unconnected mini-maps and/or chains. We have no way so far of doing anything else with them, like aggregation. We have no way of encoding multiple causation.

In fact, even classic QuIP goes beyond this.

31.4.1 Extension 1: Combining causal fragments from different sources: same item

There is an easy extension to this approach as already implemented in “classic QuIP”.

When two propositions from two different causal fragments can be considered more or less the same, create the combined map: join up the pieces on the common items. As discussed elsewhere there are four possibilities:

Chaining. (The common proposition is an influence in one fragment and a consequence in the other.)
Shared influence. (The proposition is an influence in both fragments; unproblematic.)
Shared consequence. (The proposition is an consequence in both fragments; what arithmetic do we use for this? The result doesn’t have to be consistent: E was caused by B but no, it was caused by C? The composite map can’t be considered as a larger claim that things are like this, only as an aggregate of different claims)
Shared arrow. (Combining fragments in which there is a shared influence and a shared confluence; here the issue is how we combine the arrows, e.g. making them fatter and saying “2 citations”.)

The first two are fairly unproblematic.

There is also the problem of the meaning of an individual item when it appears in, say, 20 different fragments from 20 different sources. Is it still a proposition, but a new one? Does it say “yields increased (for 20 farmers)”? Does it generalise to “yields in this area increased”? Does it merely say “yields increased (in 20 different cases)”?

[More to discuss here]

31.4.2 Extension 2: Subsuming items under more general items

This is also a part of classic QuIP. It makes it much easier to aggregate fragments, as above, by recoding different but similar items into broader categories.

There are some issues here too though. If we have

Heavier rains have led to worse crops

as well as

Hotter temperatures have led to drier ground

can we recode the left-hand side as “climate change” in both cases? It is not actually reflecting what the respondents said; they weren’t talking about climate change, just rains or temperatures.

[More to discuss here]

31.4.3 Extension 3: Recoding items from different sources as gradations of more general items

(Respondent P:) here in village Q, the new seeds have doubled our yields

(Respondent R:) here in village S, the training has slightly increased our yields

I don’t think classic QuIP does this. In classic QuIP, all we can do is this:

… which can then be combined into one map.

This is a bit of a fudge, because the meaning of “increased yields” changes depending on how you look at it. It isn’t clear does it mean “at least some increase, no matter how small” or “some average-ish increase”?

The extension I suggest here allows us to explicitly encode the degree of a relationship:

We have discussed this before, perhaps using a notation like “strength=.3” instead of “weaker”.

Here we have two separate causal fragments from separate sources which we have combined afterwards using the “shared consequence” rule. The important (implied) step was first to recode this

as this

We still have propositions, and causal claims about simple links between them. But in the aggregated map we have combined two propositions into one. Creating something like a proto-variable. This trivial-seeming trick allows us to combine maps on propositions which are in a sense common, but differ by degree, without losing the information about the degree.

31.4.4 Extension 3a: allowing negative gradations

If we are going to go along with extension 3, there is no reason not to allow negative strengths too.

So we can encode this

(Respondent P:) here in village Q, the new seeds have doubled our yields

(Respondent R:) here in village S, the weather has made our yields slightly worse

as this:

This extension does however highlight the problem of the meaning of an aggregated item which represents “the same” item in several original sources; we don’t in general even necessarily know whether to phrase it as “increased yields” or “decreased yields”. We are really only justified in saying “changed yields”. We should not be trying to make an actual statement about any change in the total yields amongst many farmers. We don’t have enough of the right kind of data for that.

31.5 That’s still not enough

Above, we aggregated mono-causal links or chains into maps with multiple links to individual items. But that isn’t the same as encoding individual respondent statements which themselves make claims of multiple causation.

I’ve had a good hack through the Save the Cow transcripts and these cases come up just too often and there is no adequate way to code them at all.

31.5.1 No way to encode explicit claims of multiple causation

The small government subsidy helped, but it wasn’t enough. Due to big price rises, my available income still went down a bit.

We can’t encode that as

subsidy --> available income increased

price rises --> available income decreased

because we’d be contradicting ourselves about available income.

We can encode it as

subsidy + price rises --> available increase decreased a bit

but then the left-hand side is just a monolithic block. We can’t get at the bits, for example we can’t combine it with another map which just mentions the subsidy.

31.5.2 No way to encode implicit claims of multiple causation

The river pollution levels have risen a lot; one part of the reason is that factory over there.

The respondent is a witness to both propositions, but the causal claim is of a contribution to a whole. Factory B did not cause much worse pollution. There is an implicit claim that there are other causes, that the contributions add up in some way, and that the net effect is a large one.

We could chicken out and just code like this:

in which the “pollution worse” is ambiguous about how much worse. The contribution is small while the net effect is large; which claim is being made? To understand the consequence item, we have to shift between the two interpretations.

31.6 Solution: propositional claims about contributions, and assume additive causation

The small government subsidy helped, but it wasn’t enough. Due to big price rises, my available income still went down a bit.

We can encode that like this:

Here we are encoding the influence of two propositions on a third. All three propositions are simple and true. But where necessary, we explicitly note that the consequence items are contributions rather than end results.

We haven’t explicitly coded the fact that the respondent said that the overall result was negative, but we can see that, from the fact that big MINUS + small PLUS = small MINUS.

We have chosen to make the distinction about the size and polarity of the influences on the arrows rather than on the items.

Our respondent can really provide evidence about each contribution, for example shows us the receipt from the subsidy and the record of shop prices.

There is no need for all the general mechanics of multiple causation; we can treat these almost like two separate causal claims. Only the word “contribution” reminds us that this consequence item can have multiple causes. This is because of the special magic of assuming that the different influences combine separately, additively, without interaction. We don’t even need to have two arrows pointing to one box.

But in practice we can treat the following as equivalent to the above:

Here, we have explicitly coded the fact that the respondent said that the overall result was negative, but we could have worked that out, from the fact that big MINUS + small PLUS = small MINUS.

You could say there are five propositions here:

got subsidy
small PLUS contribution of subsidy to available income
prices increased
big MINUS contribution of prices to available income
small resultant decrease in available income

1 causes 2, 3 causes 4, and 4 and 2 taken together cause 5 (or perhaps this is a definitional rather than causal link). In the background is an implicit causal theory which we can model in a number of equivalent ways. The simplest is probably to say that in the background there are continuous variables, and the resultant decrease is calculated according to a function which is always the same: just a generic kind of addition / subtraction.

In other words, we have used essentially the same approach as that used above to combining separate statements from separate sources which happened to mention “the same” consequence. These rules are confusingly similar, but really not the same!

I think this is as far as QuIP wants to go. It covers nearly all the tricky statements I’ve seen so far.

I think this is probably where QuIP should stop. Enough extensions already.

31.7 What these extensions still don’t do

This model allows for background causal maps in which all influences are of an additive (or subtractive) nature. Things make other things higher, or better, or worse, etc, perhaps more or less likely, and that’s it. There is no notion of the shape of the influence and (more importantly) there is no notion of any kind of interaction between multiple influences. So for example there is no room for the difference between AND and OR, see below. And there is no room for necessary or sufficient conditions.

Without wanting to, we have ended up with background theories like those common in natural science: separate, additive influences between numeric variables. This is because we wanted to keep things simple, and these kinds of models have emerged over millennia to fit that bill.

I will finish by pointing out a few of the things we can’t do.

Other vegetables don’t grow in our locality since the soil is swampy. The government agents particularly kebele principals gave support through distributing vegetables and fruits for planting. But we tried it and it couldn’t grow in our locality but it was good for people in other kebeles.

This is an explicit AND claim (you have to have seeds AND good soil). Or it’s an explicit claim that good soil is necessary but not sufficient.

31.7.1 Can’t distinguish between AND and OR

I don’t think this is a big deal. AND claims and OR claims do appear in QuIP transcripts. But not often enough to warrant a lot of attention to the difference between the two. For example, in the example of the cow and the feedstuff, it is probably enough to note that both the cow and the feedstuff have some kind of a PLUS influence on milk (though in fact the influence of one is not independent of the influence of the other).

I got the cow, and I also got the feedstuff, which I couldn’t have afforded. Thanks to both, my family now has milk.

In the example of the cow and the feedstuff, the underlying causal map is based on a conjunction; E is true if and only if B is true and C is true. There is no way we could deduce this underlying map from this single observation, and there is no way the respondent could either. The respondent is gifting us the implied underlying causal knowledge, just as they did in the simpler version of the coding rules, above. The two propositions which they report to us do not include anything about, for example, cases in which there was a cow but no feedstuff; but the implied causal map does.

This is the subtle difference to the case below: here too, all three propositions are true. As in the case above, the propositions only say that B and C are true, and E is true, and that if B and C hadn’t been true, E wouldn’t be true. But the underlying maps which we infer from the narrative and the context give us the additional information which distinguishes between AND and OR; what would happen if B was true and C false, or vice-versa.

We had no clean water, and then two different NGOs came and dug wells! We’d only really need one of them, but anyway we are happy now.

31.7.2 Necessary / sufficient conditions

Reminder:

a report of a necessary condition being fulfilled says: B happened, E happened, and B is a necessary cause of E, which means that E couldn’t have happened without B. Or: if B doesn’t happen, E doesn’t happen, but I don’t know what happens if B does happen.
a report of a sufficient condition being fulfilled says: B happened, E happened, and B is a sufficient cause of E, which means that NOT-E couldn’t have happened without NOT-B, Or: if B does happen, E does happen, but I don’t know what happens if B doesn’t happen. So in a sense a sufficient claim, like a necessary claim, is weaker than an ordinary causal claim.

We could argue: we can’t encode this kind of information, because a respondent can’t deduce something as advanced as a necessary or sufficient condition on the basis of a single story. They have to have more information, e.g. more observations, to be sure of this claim.

But we can say the same about ordinary causal claims too: they can’t be justified on the basis of a single observation or report either.

So we could code like this: B happened, and E happened, and B is a necessary cause of E. We encode the necessary/sufficient information not in the way we encode the propositions but in the way we encode the background causal information. As encoding a causal link always implicitly involves encoding the respondent’s background causal knowledge, why shouldn’t that knowledge include necessary or sufficient links too, as well as about ordinary causal links?

The biggest problem I have with actually coding these links is that whether you think of a condition as necessary or sufficient depends on the contrast you happen to be thinking of.

We really wanted milk. We have the feedstuff and an empty shed, we just didn’t have the cow. The cow was necessary, the missing piece. No other kind of help (e.g. livelihood training) would have done this.

We really wanted milk. We have the feedstuff and an empty shed, we just didn’t have the cow. The cow was sufficient. There are other kinds of help (e.g. deliveries of milk to the door) which would have done this; but the cow was enough.