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\begin{frontmatter}

\title{task set for Shinjuku project}

%\thanks{}
\author{Thomas Krichel}
%\address{ Palmer School \\ Long Island University \\
%720 Northern Boulevard \\ Brookville NY 11548--1300
%U.S.A.}
%\address{Faculty of Information Technology\\
%Novosibirsk State University\\
%Pirogov Street 2\\
%630090 Novosibirsk, Russia
%}

%\address{http://openlib.org/home/krichel \\ krichel@openlib.org}

%\begin{abstract}
%
%\end{abstract}


\end{frontmatter}


\section{Shinjuku}

The ``shinjuku'' paper, if ever done, will be an extension of the
sendai paper.  The naming of papers is pretty much random but always
uses a city name. The paper would be short, and the extension
straightforward.

Let me know if you find any mistakes.  I plan to send the paper by
early September, so that I could incorporate any comments of 
yours. 

Sendai introduces concept of the natural order, and some desirable
properties that measures that appreciate outcomes have. One of these
properties, that is not announced from the start but developed in the
paper is the respect for the natural order. I construct the ponori and
copnori measures as purpose build ``nori''s, i.e.~natural order
imposition measures. Outcomes ranked by these measure are in the
natural order.

Let us focus on copnori. The problem with the measure is described in
the test section. It's root is the constant nature of the additional
penalty. The best outcome gets penalty 0, the second best 1, the third
best 2 etc.  Thus the additional penalty is 1. What it would need to
be, is to increase (I think) as the go down. This wolud means that as
we move away from the optimal outcome, we would initially loose very
heavily, thus the dispersion of outcomes as the beginning would be
better. Thus the additional penalty, rather than being $o(x)$, say
where $o$ is the position of $x$ in the natural order, it would be
$f(o(x))$ where $f(\cdot)$ declines as $x$ incresase. 

Finding a replacement of the copnori is the first stage in Shinjuku.
The second, and possibly more trivial stage, is to unit this with
the Aselt measure as the $\nu\,l(x)+(1-\nu)\,k(x)$ formula
suggests. If we call $b$, say, this comBined expression,
we could require that $b(x\worst)=-1$. This addition 
requirment may be useful to fix some parameter values that
otherwise could be chosen arbitrarily. 

\section{Other work}

As mentioned in sendai, one could work an another version
of this paper that would really develop a full-blown
loss function and chown that, if editors make optimal
decisions, they will value the results of the system
as sugggested by the natural order. But such a 
calculation would not be part of shinjuku.

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