<s>
The	O
largest	B-Algorithm
remainder	I-Algorithm
method	I-Algorithm
(	O
also	O
known	O
as	O
Hare	O
–	O
Niemeyer	O
method	O
,	O
Hamilton	B-Algorithm
method	I-Algorithm
or	O
as	O
Vinton	O
's	O
method	O
)	O
is	O
one	O
way	O
of	O
allocating	O
seats	O
proportionally	O
for	O
representative	O
assemblies	O
with	O
party	O
list	O
voting	O
systems	O
.	O
</s>
<s>
It	O
contrasts	O
with	O
various	O
highest	B-Algorithm
averages	I-Algorithm
methods	I-Algorithm
(	O
also	O
known	O
as	O
divisor	B-Algorithm
methods	I-Algorithm
)	O
.	O
</s>
<s>
The	O
largest	B-Algorithm
remainder	I-Algorithm
method	I-Algorithm
requires	O
the	O
numbers	O
of	O
votes	O
for	O
each	O
party	O
to	O
be	O
divided	O
by	O
a	O
quota	O
representing	O
the	O
number	O
of	O
votes	O
required	O
for	O
a	O
seat	O
(	O
i.e.	O
</s>
<s>
The	O
use	O
of	O
a	O
particular	O
quota	O
with	O
the	O
largest	O
remainders	O
method	O
is	O
often	O
abbreviated	O
as	O
"	O
LR-	O
[ quota	O
name ]	O
"	O
,	O
such	O
as	O
"	O
LR-Droop	B-Algorithm
"	O
.	O
</s>
<s>
The	O
Hamilton	B-Algorithm
method	I-Algorithm
of	O
apportionment	O
is	O
actually	O
a	O
largest-remainder	O
method	O
which	O
uses	O
the	O
Hare	O
Quota	O
.	O
</s>
<s>
In	O
such	O
a	O
case	O
,	O
it	O
is	O
usual	O
to	O
increase	O
the	O
quota	O
until	O
the	O
number	O
of	O
candidates	O
elected	O
is	O
equal	O
to	O
the	O
number	O
of	O
seats	O
available	O
,	O
in	O
effect	O
changing	O
the	O
voting	O
system	O
to	O
the	O
Jefferson	O
apportionment	O
formula	O
(	O
see	O
D'Hondt	B-Algorithm
method	I-Algorithm
)	O
.	O
</s>
<s>
It	O
is	O
relatively	O
easy	O
for	O
a	O
voter	O
to	O
understand	O
how	O
the	O
largest	B-Algorithm
remainder	I-Algorithm
method	I-Algorithm
allocates	O
seats	O
.	O
</s>
<s>
The	O
highest	B-Algorithm
averages	I-Algorithm
methods	I-Algorithm
avoid	O
this	O
latter	O
paradox	O
;	O
but	O
since	O
no	O
apportionment	O
method	O
is	O
entirely	O
free	O
from	O
paradox	O
,	O
they	O
introduce	O
others	O
like	O
quota	O
violation	O
(	O
see	O
Quota	O
rule	O
)	O
.	O
</s>
<s>
The	O
largest	B-Algorithm
remainder	I-Algorithm
method	I-Algorithm
satisfies	O
the	O
quota	O
rule	O
(	O
each	O
party	O
's	O
seats	O
amount	O
to	O
its	O
ideal	O
share	O
of	O
seats	O
,	O
either	O
rounded	O
up	O
or	O
rounded	O
down	O
)	O
and	O
was	O
designed	O
to	O
satisfy	O
that	O
criterion	O
.	O
</s>
