### Prolonging Defeat (Wartime Elections)

Yesterday there was an interesting blog post by Phil Arena discussing how the costs of war are distributed within democracies. The idea behind distributing the costs of war is that,

“By shielding the average voter from the worst of war’s ravages, which they can do through a variety of strategies, not the least of which is avoiding conscription, leaders of democracies may be slip loose of the constraint electoral accountability supposedly provides.”

Phil cites Johnathan Caverley’s work which argues that during wartime states can shift the burden of war onto higher income citizens. He then extends this argument for the case of Vietnam and suggests that the U.S. not only shifted the burden from the costs of war onto higher income citizens, but also onto lower income citizens as well – creating a broad base of support from the middle class. He uses the 1972 ANES to look at the relationship between income and responding that the US should have stayed out of Vietnam, controlling for Party ID. He uses a quadratic fit and finds that,

“at least in 1972, respondents from both high income and (especially) low income households were more inclined to say that the US should have stayed out of Vietnam than were middle income voters… This suggests that democracies can potentially build a broad base of support for war among the middle class. If the human costs of war fall disproportionately on the lower class and the financial costs of war fall disproportionately on the upper class, the median voter may well indeed feel that war is cheap.”

This argument is interesting given the amount of scholarship which (in some form or another) argues that as the cost of war increases the public’s attitude toward war inevitably sours. But if the costs of war can be distributed unevenly away from the Median Voter (Middle Class), what causes their beliefs (positive or negative) about the current war? In my own research I am looking at this very question.

In a previous post I laid out a signalling game which modeled the public’s decision to keep the Incumbent (and thus continue the ongoing war) based on two distinct signals: (1) From the Media, which is potentially inaccurate but unbiased and (2) The Opposition Party, which knows the true state of the war, is biased in favor of getting elected, but also cares about the national interests. The Electorate also cares about other issues besides the war (such as the economy) which is a parameter that is know by all actors. I demonstrated that a semi-separating equilibrium exists where the war is worth continuing, the Media correctly reports that the war is worth fighting, the Opposition Party signals that they will end the war if elected, and the Electorate elects the Opposition effectively ending a war that was worth continuing. Thus, the democratic process causes the Electorate to end a war worth fighting.

In this post I want to articulate another (even more tragic) circumstance where the Democratic Process induces an unfortunate outcome. I am not going to reiterate the model here, but you can see all the details here.

### Proposition

$\exists$ a pooling equilibrium where the true value of $\omega = \underline{\omega}$; $\xi\leq 0$; O signals $\rho=c$ regardless of $\omega$; M mistakenly reports $s=h$; and E elects O with the belief $q_{h} \geq \hat{q}$, where $\frac{-(\underline{\omega} + \xi)}{\overline{\omega} - \underline{\omega}} \equiv \hat{q^{e}}$

In words, this says there can be instances where the true state of the war is not worth fighting, the Media incorrectly reports that that the war is worth fighting, the Electorate favors the Opposition on issues other than the war, the Opposition Party signals that the war is worth continuing regardless of the the true state of the war, the Electorate believes the war is worth fighting and votes  for the Opposition Party, which then continues a war which is actually not worth fighting.

This occurs because of the Opposition’s desire to get elected. will elect elect I when O sends signal $\rho = c$ iff: $q_{h}^{c} (\overline{\omega} + \xi) + (1-q_{h}^{c}) (\underline{\omega} + \xi) \geq q_{h}^{c}(\overline{\omega}) + (1 - q_{h}^{c})(\underline{\omega}) \Rightarrow \xi \geq 0$. In other words, E elects I if they favor them on issues other than the war when the Opposition signals the war should continue. This is untrue by definition. However, what if the Opposition signaled to end the war?  E will elect I when O sends signal $\rho = e$ iff: $q_{h}^{e}(\overline{\omega} + \xi) + (1- q_{h}^{e})(\underline{\omega} + \xi) \geq 0 \Rightarrow q_{h} \geq \hat{q^{e}}$, which we have assumed to be true. Thus, because the Electorate believes the war to be worth fighting, they will elect the Incumbent when the Opposition signals to end the war. Thus, the Opposition – in order to get elected – signals they will continue a war that they know isn’t worth fighting! For good measure we can see that  O will abide by the stipulated strategy iff: $\beta+(\omega \iota) \geq \omega \iota \Rightarrow \beta \geq 0$. This will be true for any value of $\omega$ and $\iota$. Again, see the previous post for to understand the parameters of the model.

The beliefs the Electorate must hold for this equilibrium are their beliefs prior to seeing the Opposition’s signal but after they have seen the Media’s signal or,

$q_{h} = Pr(\omega = \overline{\omega} | s = h) = \frac{\alpha q}{\alpha q + (1 - \alpha) (1-q)}$

$q_{l} = Pr(\omega = \overline{\omega} | s = l) = \frac{(1 - \alpha)q}{(1 - \alpha) q + \alpha (1-q)}$

### Discussion

The above equilibrium demonstrates a tragic outcome where a war that is not worth fighting is continued by the next administration. The costs of war will continue to mount and the public will support the war because they believe their side is winning. This instance is interesting in the context of research by Gelpi, Feaver, and Reifler which have have shown evidence for the hypothesis that while the public is adverse to casualties, the tolerance for the human costs of war are shaped by two attitudes: (1) Whether the war justified and (2) Whether the war is likely to be a success – the later being more important than the former. In this case the public is led to believe that the war is likely to be a success, when in reality defeat may be imminent. What causes this? Again, it is the democratic process, specifically the Opposition Party’s desire to get elected.

I am not arguing that the costs of war are unimportant. However, I am arguing that there is more to the story – specifically the way the pubic forms their beliefs based on elite cues. The “reality” the public sees may be a function of the democratic process and not “reality” at all.