Selfridge-Conway Division Procedure

Introduction

Selfridge-Conway division procedure is aimed to be envy-free. In other words, following this procedure left the participants without any envy subsequent to the completion of division and he/she will not have any envy for others. The Selfridge Conway division procedure presents method of envy free division for participants equal to three. It is named after independent discovery of John Selfridge and John Horton Conway both of whom presented it in 1960. This process was distinct envy-free method first developed for three players. A procedure ais aenvy-free aif aEACH acontainer aBelieves athat a(According aTo ameasure aict) aNo aOther arecipient areceived amore athan awhat ahe ahas. aThe amaximum anumber aof acuts ain athe aprocedure ais a5. aThe adivision ais anot aalways contiguous.

The Procedure

Case for an envy-free scheme where n = 3.

•Step 1: Player a1 acuts athe acake ainto, awhat ain ahis aview, ais a3 aequal apieces.

•Step a2: aPlayer a2, aif ahe athinks aone apiece ais alargest, atrims afrom athat apiece ato acreate awhat ahe abelieves ais aa a2-way atie afor alargest apiece. a aThe atrimmings aare aset aaside. a aIf aplayer a2 athinks athat athe aoriginal asplit awas afair, ahe adoes anothing.

•Step a3: aPlayer a3 amay achoose aany apiece.

•Step a4: aPlayer a2 achooses aa apiece. aIf athe atrimmed apiece aremains, ahe amust achoose ait. a aIf anot, ahe achooses athe aone ahe afeels ais atied awith athe atrimmed apiece afor alargest.

•Step a5: aPlayer a1 agets athe aremaining apiece.

We aare anot adone asince athere amay abe atrimmings ato adistribute, abut alet's aexamine athe aquestion aof aenvy. a aPlayer a3 ais anot aenvious asince ahe ahad afirst achoice. a aPlayer a2 ais anot aenvious asince ahe acreated aa a2-way atie afor afirst aand aat aleast aone aof athose atwo apieces ais aavailable awhen ait ais ahis aturn ato apick. a ...