Interesting question.
At the risk of explicitly disobeying your request, I'm going to link to my answer which makes the case in reference to Hobbes and Rousseau, that how we interpret 'human nature' says a lot about our own internal experiences of ourselves: Does Freudian/Lacanian psychoanalysis drives toward irrationalism and low self-control?
Our decision making can often be understood often using game theory, including moral choices. But I'd argue that our moral reasoning, is grounded in intersubjectivity: what an abstract or universal person ought to do. Discussed here, how this is the pervasive mode underlying moral thinking: Is the Categorical Imperative Simply Bad Math? :) How we view human nature, and what kinds of social systems we are capable of building, can be understood as closely linked. I interpret deeping intersubjectivity to Peter Singer's picture of the direction of moral progress, here: Studies exploring the rationale of gender equality
I would suggest 'the people' is a term defined by those in a moral community (a term from sociologist Emile Durkheim).
This can be understood in terms of Durkheim's picture of religious behaviours, as defined by groups being bound together by shared attitudes to sacred (but not necessarily conventionally religious) things, like say citizenship, ethnic identity, or festivals books vows rules or enactments of rituals. Discussed here: Why would God condemn all and only those that don't believe in God? It's interesting to note the ecclesia as in ecclesiastical, was a Greek place to gather and vote.
Or in terms of social contract theories, where people take on burdens and restrictions associated with living in community, to recieve collective benefits. Rights discourse is an impactful way we can understand the social contract in practice and it being revised, like the Universal Declaration of Human Rights, and what esteem it is held in or not is an interesting case, especially contrasted to the Soviet world with a different relation between citizen and state. Durkheim's picture helps understand how challenging what the group holds sacred, can challenge the group's cohesion.
Or you can use game theory to think about maintaining unstable game-theoretic equilibria and managing free-rider generated instabilities. Discussed inc link to social contracts here: Is the tyrannicide perpetrated by William Tell morally legitimate?
I can't help but think a close study of history will be the biggest source of insight. I see moments of political contention by fairly balanced forces as key to how 'the people' have been able to define themselves, like Cleisthenes reforms after the attempt to end Ancient Athenian democracy, the seccessio plebis in Rome and
the Conflict of the Orders, and the Baron's Revolt and habeus corpus. I like Durkheim's picture of collective effervescence, which I see as something with an underappreciated role in history, whether it's melas in India, or Burning Man.
We can learn a lot from failure. Like James C. Scott's 'Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed', and Joseph Tainter's 'The Collapse of Complex Societies'. The cohesion of a group depends on having leaders who build on what makes the community and it's cohesion work, which as Scott notes we may be impossible to fully analyse. And as Tainter points out, unknowable future crisees will reveal whether the capacities of a group can rise to meet new challenges, and if not may result in 'rapid simplification', and decohesion of the group, and loss of their way of life.
