<s>
Chore	B-Algorithm
division	I-Algorithm
is	O
a	O
fair	O
division	O
problem	O
in	O
which	O
the	O
divided	O
resource	O
is	O
undesirable	O
,	O
so	O
that	O
each	O
participant	O
wants	O
to	O
get	O
as	O
little	O
as	O
possible	O
.	O
</s>
<s>
Whereas	O
in	O
chore	B-Algorithm
division	I-Algorithm
,	O
there	O
are	O
different	O
chore	O
types	O
and	O
different	O
amounts	O
of	O
time	O
needed	O
to	O
finish	O
each	O
chore	O
.	O
</s>
<s>
The	O
chore	B-Algorithm
division	I-Algorithm
problem	O
was	O
introduced	O
by	O
Martin	O
Gardner	O
in	O
1978	O
.	O
</s>
<s>
Chore	B-Algorithm
division	I-Algorithm
is	O
often	O
called	O
fair	O
division	O
of	O
bads	O
,	O
in	O
contrast	O
to	O
the	O
more	O
common	O
problem	O
called	O
"	O
fair	O
division	O
of	O
goods	O
"	O
(	O
an	O
economic	O
bad	O
is	O
the	O
opposite	O
of	O
an	O
economic	O
good	O
)	O
.	O
</s>
<s>
To	O
use	O
the	O
last	B-Algorithm
diminisher	I-Algorithm
protocol	O
:	O
ask	O
an	O
agent	O
to	O
cut	O
a	O
piece	O
worth	O
exactly	O
for	O
him	O
.	O
</s>
<s>
To	O
use	O
the	O
Even	B-Algorithm
–	I-Algorithm
Paz	I-Algorithm
protocol	I-Algorithm
:	O
ask	O
each	O
agent	O
to	O
mark	O
the	O
half-value	O
line	O
,	O
making	O
sure	O
all	O
lines	O
are	O
parallel	O
.	O
</s>
<s>
An	O
example	O
is	O
the	O
Austin	B-Algorithm
moving-knife	I-Algorithm
procedure	I-Algorithm
,	O
which	O
guarantees	O
each	O
partner	O
a	O
piece	O
that	O
he	O
values	O
as	O
exactly	O
1/n	O
of	O
the	O
total	O
.	O
</s>
<s>
in	O
the	O
Selfridge	B-Algorithm
–	I-Algorithm
Conway	I-Algorithm
protocol	I-Algorithm
)	O
.	O
</s>
<s>
It	O
is	O
similar	O
to	O
the	O
Selfridge	B-Algorithm
–	I-Algorithm
Conway	I-Algorithm
protocol	I-Algorithm
,	O
but	O
more	O
complicated	O
:	O
it	O
requires	O
9	O
cuts	O
instead	O
of	O
5	O
cuts	O
.	O
</s>
<s>
Using	O
Austin	B-Algorithm
moving-knife	I-Algorithm
procedure	I-Algorithm
,	O
divide	O
piece	O
1	O
to	O
two	O
slices	O
that	O
partners	O
1	O
and	O
2	O
consider	O
equal	O
.	O
</s>
<s>
It	O
is	O
analogous	O
to	O
the	O
Brams	B-Algorithm
–	I-Algorithm
Taylor	I-Algorithm
procedure	I-Algorithm
and	O
uses	O
the	O
same	O
idea	O
of	O
irrevocable	O
advantage	O
.	O
</s>
<s>
Peterson	O
and	O
Su	O
gave	O
a	O
moving	O
knife	O
procedure	O
for	O
4-person	O
chore	B-Algorithm
division	I-Algorithm
.	O
</s>
<s>
provided	O
the	O
first	O
discrete	O
and	O
bounded	O
envy-free	O
protocol	O
for	O
chore	B-Algorithm
division	I-Algorithm
among	O
any	O
number	O
of	O
agents	O
.	O
</s>
<s>
Simmons	B-Algorithm
–	I-Algorithm
Su	I-Algorithm
protocols	I-Algorithm
.	O
</s>
<s>
Su	O
showed	O
,	O
using	O
a	O
dual	O
lemma	O
,	O
that	O
a	O
similar	O
protocol	O
can	O
be	O
used	O
for	O
approximate	O
envy-free	O
chore	B-Algorithm
division	I-Algorithm
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
shows	O
that	O
there	O
always	O
exists	O
an	O
envy-free	O
chore	B-Algorithm
division	I-Algorithm
with	O
connected	O
pieces	O
.	O
</s>
<s>
Heydrich	O
and	O
van	O
Stee	O
calculate	O
the	O
price	O
of	O
fairness	O
in	O
chore	B-Algorithm
division	I-Algorithm
when	O
the	O
pieces	O
have	O
to	O
be	O
connected	O
.	O
</s>
<s>
It	O
may	O
be	O
possible	O
to	O
use	O
chore	B-Algorithm
division	I-Algorithm
procedures	O
to	O
divide	O
up	O
the	O
work	O
and	O
cost	O
of	O
reducing	O
climate	O
change	O
among	O
nations	O
.	O
</s>
<s>
However	O
,	O
using	O
chore	B-Algorithm
division	I-Algorithm
procedures	O
reduces	O
the	O
need	O
for	O
a	O
supra-national	O
authority	O
to	O
partition	O
and	O
oversee	O
work	O
by	O
those	O
nations	O
.	O
</s>
<s>
Another	O
use	O
for	O
chore	B-Algorithm
division	I-Algorithm
would	O
be	O
in	O
the	O
rental	B-Algorithm
harmony	I-Algorithm
problem	O
.	O
</s>
