Gaudenz Steinlin <gaud...@debian.org> writes:

> I'm not sure if I interpret your PDF graph correct. Do you suggest that
> everyone on the same line forms a cohort and should have the same
> priority?

Yes.

> If so I don't understand how those that don't have any outgoing edges in
> the (reduced) graph get there level. It looks like they are just moved
> to the highest possible level. But is that really what we want?

People get pushed down by incoming edges. So yes, we fund people as soon
as we have funded everyone who is obviously more deserving.  I mentioned
at the end it might be worth having cutoffs for the two factors (need,
contribution) to avoid people being pushed up too far.  In the actual
test data I think the levels work out more or less sensibly.

>
> Or to put it another way, why are number 29 and 36 ranked higher than 19
> and 7. According to the ordering specified above there is no clear
> justification for this.

29 and 36 are ranked higher because after we have funded 1-5, 28, they
are "sources"; nobody else is "clearly better".

> It seems to me this problem arises because your graph drops edges over
> more than one level.

No, that's definitely not the cause. The ranking uses all of the
edges. Only the edges to the next level are drawn because it makes the
picture less crowded, and because it's enough to provide a "witness" for
why someone is _not_ funded. For example it provides an easily checkable
way of seeing why 10 is in the fifth cohort.

>  I'm not sure if this is really the case, but the graph looks like
> results in contribution taking precedence over need. Is that correct
> and intended?

Not exactly. It (implicitely) provides a way of mixing the two factors
in making a decision.  If we insist on lexicographic ordering (need
taking strict precedence over contribution) then we would fund 18 before
e.g. 19-21, which doesn't seem like what we'd want.

Compared to choosing some weights, the scheme I've proposed has some
pros and cons.

The main con, is that it's a bit more complicated. For me, it's easiest
to understand as a process/algorithm of going through the "queue",
making sure we don't fund obviously less deserving (leaving aside the
subjectivity of the numbers) people first.

On the plus side, it's much more transparent than a set of weights
arrived at by the bursaries team in secret. It's also independent of the
actual numerical scales used in the ranking.  This gives us flexibility
to experiment with different scales for need and contribution without
reworking a set of weights.  It has seemed to me in the past that these
weighting schemes have a strong effect on who gets funded. Of course we
can "fine tune" the weights until the results "make sense", but then we
are getting closer to a completely subjective ranking, since we just
adjust the weights until the ranking agrees with our gut feelings.

Another important plus is that the core rule (a definitely better than
b) is easy to reach concensus on.

One concern you bring up is that this scheme maybe doesn't do enough to
prevent "undeserving" people being funded (at least, that's my
interpretation of your comment about people being moved to the highest
possible level).  I'm not sure if that's a problem in practice, but a
possible way of addressing it would be to choose a cutoff for one or
both factors so that in the absence of budget constraints we'd find it
acceptable to fund everyone remaining on the list. My gut feeling is
that such a cutoff would keep roughly everyone eligible for food and
accomodation funding, but note that f+a funding does not currently take
into account financial need.

d



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