Interesting study. I'm wondering though why a democracy would have any more advantage at the bargaining table in an international crisis than an autocratic regime.
The results of your study seem to suggest that there are two scenarios once the democracy has made the commitment to intervene:
1) The democracy has the upper hand in the conflict, and there is domestic pressure to follow through on the conflict
In this case, I don't really see how the domestic pressure would give any additional advantage to a democracy at the bargaining table. The democracy is already winning the conflict, so it is likely that they will gain concessions from the other party. Pressure one way or the other might influence whether or not the opposition thinks they can sustain a long term conflict, but when you consider the options an autocratic regime has in an identical situation, it seems to become moot. An autocratic regime, unlike the democracy, faces little to no internal pressure, so it can choose to either continue the conflict or end it. Considering that it is already winning, the logical choice is to continue until it gains the concessions it wants. So really, there is no difference in this case between an autocratic regime and a democracy. Both types of government are encouraged to follow through on the conflict. One by popular opinion, the other by logical choice.
2) The democracy is losing the conflict, and there is domestic pressure to follow through
For the sake of this argument, let's say that the government in question is unlikely to incur further gains from continuing the conflict (escalating the conflict will not "turn the tide"). In this case, the democracy would seem to be severely inhibited at the bargaining table. It wants to minimize its losses, but at the same time, it has domestic pressure to continue the war, which would be futile. At the same time, the ruler of the autocratic regime faces no such pressure, and he is free to choose the logical course of action, which is to prematurely end the conflict to avoid incurring further losses. So in this case, it would seem that the autocratic ruler has the advantage.
To sum up:
Option 1:
The democracy gains further impetus for following through on conflict and gaining extra concessions, but this conclusion is already reached by the logic of the situation, the consent of the public is only a confirmation of the correct choice and makes no actual difference at the bargaining table
Advantage: Neither
Option 2:
The democracy is inhibited from following the logical course of action by public opinion, while the dictator is free to minimize losses without public recourse
Advantage: Autocratic Regime
Now, this just applies to the situation if the democracy has already made the commitment. If you are talking about negotiations in which the democracy is threatening a commitment, things come out a little differently. To me, the results of your survey seem to suggest that the public's opinion on whether or not to intervene is heavily contingent on whether or not they think victory is possible. This would require a different study, but I think the results would be pretty obvious.
Now, if we were to translate this into a hypothetical negotiation, similar results to the post-invasion situation would emerge. The following scenarios assume that all actors are capable of making close approximations of the likely outcomes of armed conflicts. If they are not able to do so, then the whole scenario is just psychological guesswork based on intelligence reports of enemy military strength.
1) The democracy is attempting to gain concessions from the autocracy, and the conflict is winnable
i) The opposing party believes victory is unlikely
Assuming that accurate power calculations are being made on both sides, the outcome will likely be that the democracy gains concessions, as it is willing to enter a conflict it believes it will win, and the opposing party is unwilling to enter a conflict it believes it will lose. Again, limited utility is gained from the consent of the public, as the negotiating position of the opposing party is wholly predicated on its calculation of the likely outcome. Whether or not the public supports the president is irrelevant, as public support inherently implies (based on my earlier inference from your study's results) that success is likely. If this is the case, the success of the opposition party is unlikely, and the results are the same as the situation above. Of course, this leaves out one possibility, which is that the president is lying to the people and is bluffing to try to gain concessions. In this situation, it would seem that the president gets an extra boost in negotiating from the public, but assuming that the leader of the opposition is rational, and has made a close approximation of the true disparity of relative military strength, he would know that his success is likely, and the negotiations would again deadlock.
2) The democracy is attempting to gain concessions from the opposing party, and victory is unlikely.
i) The opposing party believes victory is likely
I covered this a little bit above. The president can either back down, knowing that he cannot win the conflict, or try to bluff. The results would be in both cases that negotiations deadlock, as the results are entirely predicated on the mindset of the opposing force, and in this case, the opposing force believes victory is likely. Assuming he has made an accurate power calculation, he shouldn't be swayed by public opinion in the democracy or the bluster of the President.
For an autocratic regime unswayed by public opinion, the results would not be any different. He still has the option of bluffing, but unlike the democracy, he does not need the approval of the public to follow through, so it makes no difference. In any of the other situations, the results would be the same. If the autocrat believed he could win, and the opposing force believed it would lose, then there would be concessions. If the reverse occurs, then a rational dictator would leave the negotiating table.
So basically, in this entire scenario, I think it is clear that the driving force behind negotiations is the power calculations made by both sides. Considering that public opinion in one nation has no effect on that, I think that there is no advantage for a democracy over an autocratic regime. Obviously I have made a big assumption that both sides can make accurate power calculations. But even if that were not true, I still believe that the autocratic regime is still capable of bluffing just as well as a democracy, it just doesn't need public support. In the end, there is no net gain at the negotiating table.
Anyways, sorry for the rambling post. Your study was very thought provoking and I'd love to hear your input on the scenarios I've just laid out.
