Hmm. I'm not sure i've understood your question correctly, but let me try to respond, and see whether this answer satisfies in any way....!
In complex systems, any noticeable impact will have lots of different causes (which are themselves effects of other causes). Therefore, awarding 'prizes' to some people/organisations/programmes in that complex system on the basis that they created 'impact' has the strong potential to end up rewarding people who contributed little, and maybe missing people who did crucial (but behind the scenes) work.
In addition, evidence suggests that the act of prize giving will distort people's behaviour in ways which are detrimental to the creation of real impact - people will focus on doing the things that are noticeable, rather than the things that are important. And, in the end, they may end up doing things solely for the prizes, rather than for the impact they create.
When can you identify the impact that a particular person/team/organsiation/programme has? When the causal chains are short. i.e. when doing X reliably leads to Y. In those circumstances, if what you care about is Y happennig (and only Y happening) then by all means seek to monitor for examples of X behaviour and reward it.
For me the key question is: what is the relationship between 'desired impact' and how activity is managed in order to see that we get 'more' of it?
Your school prize example is actually really interesting. As you say, we want children to have positive influences on one another. Let's say that is impact in the world that we want to see more of. What are the ways that a school could be managed to develop more of that behaviour by the children?
- Presumambly, the children need to be involved in a conversation about what being a 'good influence' entails - as there are likely to be many different versions of what being 'good' in this way looks like amongst pupils in a school (e.g. one family might think that being a good influence requires encouraging a particular religious practice, others may hold opposite views)
- Then maybe a conversation with the children about what motivates them to be a good influence on others. Do they do that because they are kind? Because they seek reward/affirmation? Because its the right thing to do?
- From these conversations, a school could explore how might recognise and affirm examples of this behaviour. Would this involve reprting of positive infuence by other puipls? (generating a risk of collusion) would it rely on teachers witnessing a 'good influence' activity (maybe leading to performative goodness in front of teachers, but not elsewhere)? would it involve an actual prize (risking leading to the crowding out of intrinsic motivation)? Or simply recogntion and acknowledgement of the good act? (risking 'so what').
My question from all of this - how would you experiment and learn to see how you could manage a school in ways so as to create the conditions where more pupils were positive influences on each other?
(I feel like i've disappeared down a school prize rabbit hole, so maybe i'll stop there!)