I think of self-esteem as a thermometer. It's a measure of something (Your value as a person? More narrowly, your deserved social status?)

What do you mean by "deserved" social status? Status is decided by those that grant it. And if people decide to grant status to Joe because Joe coerces them to, Joe's status is granted by his peers and thus deserved. That is, self-esteem is your vision of the esteem others give you.

Now, is Joe someone you or I would like to be around? No. But that doesn't mean he has low self-esteem, or that he isn't proud of himself.

Along slightly different lines, look at self-esteem as self-description. If I describe myself as "good-looking," and someone points out that my ears are grotesquely large, that will conflict with my self-description. If I describe myself as "bad-looking," the same comment with reinforce my self-description. If I describe myself as "assertive" and someone cuts in front of me, in order to maintain that description I need to rebuke them. If I describe myself as "submissive," then when someone cuts in front of me I might sigh, but if I do more it'll conflict with the self-description.

Typically, when converting self-description to self-esteem, one would say that good-looking is higher than bad-looking, and assertive is higher than submissive. A bully halts criticism and commands respect- the features of being held in high esteem- but obtains that esteem through violence and domination. At each instant, when someone is deciding how to respond to praise or an insult, they don't have time to run a calculation of which response will work better for them: they consult their self-esteem and see if what's happening matches what they expect to happen.