At first it seems like a mixture of desire and belief in a possibility. It’s not just desire because you can ‘have your hopes too high’, though the hoped for outcome is well worthy of desire, or ‘abandon hope’ when something reaches some level of unlikelihood. But hope is also not linked to a particular level of chance. It implies uncertainty about the outcome, but nothing beyond that.
Is it a mixture of significant uncertainty and a valuable outcome then? No, you can consider something plausible and wonderful, but not worth hoping for. Sometimes it is worse to hope for the most marvelous things. No matter how likely, folks ‘don’t want to get their hopes up’ or ‘can’t bear to hope’ .
So there is apparently a cost to hoping. Hopes can bring you unhappiness if they fail, while another possibility with similar chances and desirability which was not hoped for would cause no distress. So hope is to do with something other than value or likelihood.
A hope sounds like a goal which you can’t necessarily influence then. Failing in a goal is worse than failing in something you did not intend to achieve. A hope or a goal seems to be particular point in outcome space where you will be extra happy if it is reached or surpassed and extra unhappy otherwise. We seem to choose goals according to a trade-off of ease and desirability, which is reminiscent of our seemingly choosing hopes according to likelihood and desirability. Unlike hopes though, we pretty much always try harder for goals when the potential gains are big. This probably makes sense; trying harder at a goal increases the likelihood of success, whereas hoping more does not, yet still gives you the larger misery of failure.
Why hope at all then? Why not just have smooth utility functions? Goals help direct actions, which is extremely handy. Hopes seem to be outcomes you cheer for from the sidelines. Is this useful at all? Is it just a side effect of having goals? Is it so we can show others what would be our goals if we had the power? In which case should we expect declared hopes to be less honest than declared goals? Why are hopes so ubiquitous?
Meteuphoric 
Some hopes seem to be connected with outcomes that we have a little influence over but not much. For example, you might enter a contest and hope to win a prize, but your chances are slim because outcome is under control of the judges, not you. Hoping to win means you will work harder at it, while recognizing that it’s largely not under your control. (Another example would be the hope that someone will find you attractive.)
Optimistic people overestimate their influence, so we say they’re more hopeful. Or you could put it the other way and say that pessimistic people underestimate their influence.
I think that hope is analogous to credit. You’re borrowing the potential happiness of tomorrow, for happiness today. If you ‘put your hopes too high’ then that means you are borrowing more happiness then what you are likely to be able to pay off.
If the goal you are directing your hope towards ends up failing, then you you are left with an emotional debt that must be payed. However if you are able to use hope successfully, then you smooth out your utility curve, allowing you to be happy today even if you currently have no reason to be.
Hoping can be a net positive, even if the thing doesn’t occur. Hoping and savouring an imagined better future is enjoyable in itself.
Summary: we don’t know why we hope.
people express hope as they move away from what they really want
so its a distance from what you really want that is from what you really are
[not superficially want such as to keep power within the group]
thus a distance that can be calculated and approximated