There's a distinction between what I believe is more likely to be true, and what I wish were true instead. The null hypothesis is always more likely to be correct than any specific hypothesis. If I have to stick with a very unpredictive hypothesis, I have a decreased ability to predict the world, I will therefore do worse.

In this case, I am fairly sure that the near/far distinction gives good reason to believe that the Israel experiment doesn't contradict the cave man fight: i.e. what people do in far situations can be the opposite of what they do in near situations.

But as to why people root for the underdog, rather than just choosing at random... I am less sure.

The empathy argument has been made independently a few times, and I am starting to see it's merit. But empathy and signalling aren't mutually exclusive. We could be seeing an example of exaption here - the empathy response tended to make people sympathize with the underdog, and this effect was re-enforced because it was actually advantageous - as a signal of virtue and power.

Yes, it could be. But "random side effect of unspecified other optimizations" is a completely general explanation for any trait of any organism, so as a hypothesis it is totally uninformative.

The obvious "random side effect" theory, for underdog-empathy, is that we tend to empathize with agents who feel the way underdogs feel (e.g., in pain, afraid, pulling together their pluck to succeed) regardless of whether the agent who feels that way is an underdog, or feels those emotions for some other reason.

To test this theory: do we in fact feel similarly about people struggling to scale a difficult mountain, or to gather food for the winter in the face of difficulty and starvation risk? Or does our empathy with underdogs (in group conflict situations specifically; not in struggles against non-agent difficulties like mountains) bring out a response that would not be predicted from just the agent's fear/pain/pluck? Also, can our responses to more complex fear/pain/pluck situations (such as the person struggling to avoid starvation) be explained from simpler reactions to the individual components (e.g., the tendency to flinch and grab your thumb when you see someone hit his thumb with a hammer)?