Signpost sequence

Generalized rounding rule From Wikipedia, the free encyclopedia

In mathematics and apportionment theory, a signpost sequence is a sequence of real numbers, called signposts, used in defining generalized rounding rules. A signpost sequence defines a set of signposts that mark the boundaries between neighboring whole numbers: a real number less than the signpost is rounded down, while numbers greater than the signpost are rounded up.[1]

Signposts allow for a more general concept of rounding than the usual one. For example, the signposts of the rounding rule "always round down" (truncation) are given by the signpost sequence

Formal definition

Summarize
Perspective

Mathematically, a signpost sequence is a localized sequence, meaning the th signpost lies in the th interval with integer endpoints: for all . This allows us to define a general rounding function using the floor function:

Where exact equality can be handled with any tie-breaking rule, most often by rounding to the nearest even.

Applications

In the context of apportionment theory, signpost sequences are used in defining highest averages methods, a set of algorithms designed to achieve equal representation between different groups.[2]

References

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