Irrational? Yes.

Needed? Yes.

When somebody has nothing, or thinks they do, and there's no indication that it will change any time soon, sometimes the only thing that will keep them going is clinging onto some sort of hope.

Hope refers to a belief in a positive outcome. The question of whether hope is rational is directly dependent on whether the belief is a rational. This is difficult to answer for the following two reasons; one, it depends on whether the basis for the belief is rational or irrational, and two, whether the belief is rational or irrational can differ between individuals, even if the individuals under consideration evaluate the likelihood of a outcome in a rational way!

We can, however, arrive at a tentative answer if we analyze beliefs in the context of a Bayesian model for an individual's beliefs. In a Bayesian model, an individual's beliefs can be modeled in terms of a collection of claims and the likelihood that an individual assigns to those claims. A belief is the likelihood that the individual assigns to a given claim. The individual's present beliefs are dependent on three things: the likelihood that the individual assigns to a claim, the experiences of the individual, and the degree to which the individual's experience affect the likelihood he/she assigns to a claim.

Whether a belief is rational is highly dependent on the individual's experience and the degree to which the individual's beliefs are affected by that experience (see note). It is reasonable to expect that an ideally rational individual with little experience with regard to a given claim should not assign a strong likelihood to that claim, and an ideally rational individual with much experience with regard to a given claim should not easily alter the established likelihood for that claim.

My past experiences with individuals (which I admit is limited compared to the entire human population) suggests that younger individuals are generally more likely to be hopeful than older individuals. This suggests to me that younger individuals (which generally have less experience with any given claim than an older individual) assign a stronger likelihood to positive outcomes than older individuals. is not the behavior I would expect for ideally rational individuals. Thus, in the context of this cursory analysis, I would say that for most individuals that possess it, hope, or the belief in a positive outcome, is irrational.

This is not to say that hope does not serve a purpose; it may very well be that hope, independent of whether we classify it as rational or irrational, may be an important mechanism that helps an individual (or a society for that matter) to survive a crisis.

Note: As an aside, we note that different experiences can produce different beliefs and can do so in a nonlinear way, so that rational individuals can disagree on the likelihood of a given claim.