[Mnet-devel] another paper

[Jim Dixon]

On Sat, 8 May 2004 zooko at zooko.com wrote:

> > 1.1  increasing (OK - the more of your own data sent the better)
> > 1.2  strictly concave
> > 1.3  Un(0) = 0 (no data transmitted, no happiness)
> > 1.4  continuously differentiable
> > 1.5  the first derivative Un'(Cn) = 0
> ...
> > Properties 1.1 and 1.3 make sense.
> >
> > The third property doesn't hold at all.  Most users deal in terms of
> > files.  If they can't transmit an entire file, then their bandwidth has
> > been burned for nothing, and they get irritated.  So Un is a step
> > function, with discontinuities spaced quite widely apart.
>
> You mean "Property 1.4 doesn't hold at all.", right?

Yes.

> > 1.2 means that as you transmit more data, the utility (happiness)
> > delivered by each additional byte decreases.  This is questionable.
>
> You mean "1.1 means that as you transmit...", right?

No.  'Strictly concave' means that the slope of the curve continuously
decreases.  In other words, each additional quantum of data transmitted
delivers less utility (less happiness) than the previous.  This makes the
mathematics work, but has nothing to do with reality.

The big failing is the requirement that the utility function be
differentiable.  It just doesn't square with experience.  Most people have
low bandwidth connections, so files take a long time to download. A CDROM
takes hours, a DVD can take days.  So satisfaction comes in chunks, and
often enough the download fails, leaving people frustrated. Or, as a
mathematician would say, utility is a step function (and so is not
continuously differentiable) and can be negative.  This does not at all
match the model in the paper.

While this all might seem esoteric, I have certainly seen its
consequences.  People get irritated with incomplete downloads (erratic
utility) and watching their machines churn moving other people's data
around (definitely negative utility), so they just stop using p2p
software.  This is not the world of the model, where utility functions
converge gracefully to everyone's benefit.

--
Jim Dixon  jdd at dixons.org   tel +44 117 982 0786  mobile +44 797 373 7881
http://jxcl.sourceforge.net                       Java unit test coverage
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