Appendix

Measured Disagreeableness

In the “Disagreeable Bet” section of chapter six (page 145), we mentioned that the reason a negotiation is more disagreeable (or agreeable) at higher tension is because horizontal shifts are disagreeable (or agreeable) to the extent that the tension changes. If the tension doesn’t change, then there’s no change in our likelihood of a fight, and so there mustn’t be anything disagreeable (or agreeable) about the new offer.

That’s a good start, but to truly calculate the total disagreeableness, one has to split the response into its two confidence components, which you can see in more detail in Figures 49 to 51.

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Figure 49. How disagreeable is any particular response?

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Figure 50. Summarizing the moral from Figure 49: How disagreeable a response is is the sum of the disagreeablenesses of its two parts. In this example, Mark provides a response (the solid pair of curves crossing at “Mark” in the rectangle) to Tim’s previous response (the dotted pair of curves crossing at “Tim” in the oval). Mark signals that he himself is more confident than Tim claimed he is (pride), and the disagreeableness of that is shown by the area labeled “a.” Mark also signals that Tim is less confident than Tim claimed (disdain), and the disagreeableness of that is shown by the area labeled “b.” They are shown as “+,” meaning a positive bet.

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Figure 51. In this example, Mark’s response to Tim is like the one in Figure 50 since Mark says Tim is less confident than Tim claimed, but it now differs because Mark claims he himself is even less confident than Tim claimed (humility). This latter claim has the area “a” on the right, and the “−” indicates that it is a negative bet—or unbet. It’s intuitively an unbet because this portion of Mark’s response corresponds to Mark suggesting a better offer for Tim than Tim suggested. Mark’s total response is the combination of both its parts and ends up overall lower in disbelief, and a bit in Tim’s favor, than what Tim suggested.

We’ll leave the details to the figures and their legends, but how disagreeable my confidence claim is concerns the area swept over when sliding from the confidence level you claimed to the confidence level I claim it to be instead. Specifically, it concerns the area swept between the other curve and the previous tension. It’s the areas shown in the figures that capture the level of disagreeableness of my correction of your confidence claim.

The more I shift the compromise horizontally, the larger the area of such a swept curve. So that fits the obvious intuition that bigger compromise shifts are more disagreeable.

But notice also that the area swept out depends on how steeply the other confidence curve is. The steeper it is, the greater the vertical component to the curvy triangular-shaped region, and thus the greater the overall area. And—this is the important part—confidence curves are steeper when tension is higher. Thus, when the tension is higher, the level of disagreeableness for any given horizontal shift is greater. That is, a bigger bet must be put at stake.

To help get a better visual impression of this key point—that, when at higher tension, emotional expressions amount to larger bets (or unbets)—consider Figures 52 and 53. They are essentially the same, showing in the shaded regions the level of disagreeableness (or agreeableness) of each of the four response confidence emotional expressions.

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Figure 52. The four regions of area quantifying the disagreeableness corresponding to the four qualitatively different confidence emotional expressions Mark can make to Tim’s last “move.” Mark can correct Tim about Mark’s own confidence, saying it is higher or lower, leading to the positive and negative “a” area regions, respectively. And Mark can correct Tim about Tim’s confidence, saying it is higher or lower, leading to the positive or negative “b” area regions, respectively. For a full response, Mark will correct Tim both on Mark’s own confidence and on Tim’s, and the total level of disagreeableness will be the sum of the two “a” and “b” areas.

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Figure 53. This conveys the same idea as Figure 52, but the only difference is that Tim’s previous response ended up shifting the negotiation to a lower tension than was the case in Figure 52. The same four emotional expressions are shown as before, each having the same horizontal compromise shift as before. But now the levels of disagreeableness and agreeableness are much lower. At higher tension levels, negotiation becomes more poker-like, because larger bets are required. But when tension levels are low, like here, the negotiation becomes less poker-like, allowing negotiation to continue without as much drama, albeit with a lower pressure for honesty.

Consider the tiny shaded-area version first, the one in Figure 53. In this figure Tim’s response—to which Mark must respond—pushed the negotiation to a point lower in the diagram than it is in Figure 52. That’s the only difference between the two figures. The diagram in Figure 53 shows the same potential response emotional expressions Mark might make to Tim as in Figure 52, but now you can see that the levels of disagreeableness—the shaded areas—are much smaller in Figure 53 compared to those in Figure 52. That is, because Tim’s previous response pushed the negotiation to a low tension, Mark can engage in disagreeable responses without nearly as much disagreeableness and can engage in agreeable responses without nearly as much agreeableness. At low tension, there’s little social capital at stake in Mark’s response (because the curves are shallower, and so the tension changes less when Mark corrects a confidence curve). Mark can make a counter without much of a poker aspect to it at all. The incentives for honesty are consequently much lower.

Now consider the comparatively giant shaded-area version of it in Figure 52, where Tim left the negotiation at high tension. If Mark is disagreeable, now it’s hugely exaggerated, requiring a huge bet of social capital; and if Mark is agreeable, that, too, is exaggerated, amounting to a large unbet. All the social repercussions are jazzed up. The poker game is on, and the pressure to be honest (and even to potentially err on the side of one’s opponent) has gone way up!

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