Robert Axelrod’s Robert Axelrod’s

TournamentsTournaments, as reported in

Axelrod, Robert. 1980a. “Effective Choice in the Prisoner’s Dilemm

a.”

Journal of Conflict Resolution 24: 3-25.

Axelrod, Robert. 1980b. “More Effective Choice in the Prisoner’s Dil

emma.”

Journal of Conflict Resolution 24 (3): 379-403.

Axelrod, Robert. 1984. Evolution of Cooperation.

Robert Axelrod’s Robert Axelrod’s

TournamentsTournaments, as reported in

Axelrod, Robert. 1980a. “Effective Choice in the Prisoner’s Dilemm

a.”

Journal of Conflict Resolution 24: 3-25.

Axelrod, Robert. 1980b. “More Effective Choice in the Prisoner’s Dil

emma.”

Journal of Conflict Resolution 24 (3): 379-403.

Axelrod, Robert. 1984. Evolution of Cooperation.

Tournament Num. 1 Tournament Num. 1 (1980)

-non-zero sum setting, given payoff matrix (R=3, T=5, S=0, P=1)-non-zero sum setting, given payoff matrix (R=3, T=5, S=0, P=1)

-round robin tournament (play all other entrants, twin, and -round robin tournament (play all other entrants, twin, and RANDOM)RANDOM)

-each entrant told to write a program to select C or D choice every -each entrant told to write a program to select C or D choice every move, can use history of the game so far in this decision makingmove, can use history of the game so far in this decision making

-sent copies of preliminary tournament in which TFT scored second, -sent copies of preliminary tournament in which TFT scored second, so known to be powerful competitor, also told RANDOM was so known to be powerful competitor, also told RANDOM was somewhere in the competition somewhere in the competition tried to improve on TFT principle tried to improve on TFT principle

-known number of moves per game: 200-known number of moves per game: 200

-entire round robin run 5 times -entire round robin run 5 times total 120,000 moves and 240,000 total 120,000 moves and 240,000 choiceschoices

Tournament Num. 1 Tournament Num. 1 (1980)

-non-zero sum setting, given payoff matrix (R=3, T=5, S=0, P=1)-non-zero sum setting, given payoff matrix (R=3, T=5, S=0, P=1)

-round robin tournament (play all other entrants, twin, and -round robin tournament (play all other entrants, twin, and RANDOM)RANDOM)

-each entrant told to write a program to select C or D choice every -each entrant told to write a program to select C or D choice every move, can use history of the game so far in this decision makingmove, can use history of the game so far in this decision making

-sent copies of preliminary tournament in which TFT scored second, -sent copies of preliminary tournament in which TFT scored second, so known to be powerful competitor, also told RANDOM was so known to be powerful competitor, also told RANDOM was somewhere in the competition somewhere in the competition tried to improve on TFT principle tried to improve on TFT principle

-known number of moves per game: 200-known number of moves per game: 200

-entire round robin run 5 times -entire round robin run 5 times total 120,000 moves and 240,000 total 120,000 moves and 240,000 choiceschoices

14 Entrants14 Entrants-3 countries, 5 disciplines (psychology, math, economics, sociology, -3 countries, 5 disciplines (psychology, math, economics, sociology,

political sciences)political sciences)

-scores range from 0 to 1000, but “useful benchmark for very good -scores range from 0 to 1000, but “useful benchmark for very good

performance is 600,” attained if both always cooperate togetherperformance is 600,” attained if both always cooperate together

-“very poor performance [benchmark] is 200 points” (if both always -“very poor performance [benchmark] is 200 points” (if both always D) D)

-winner Tit for Tat (TFT) scored 504 (but if change P=2, does not -winner Tit for Tat (TFT) scored 504 (but if change P=2, does not win)win)

-top 8 entries were nice (defined as not first to defect), rest were -top 8 entries were nice (defined as not first to defect), rest were notnot

-nice entries’ scores scored from 472 to 504, while best of mean -nice entries’ scores scored from 472 to 504, while best of mean entries only scored 401 points (huge disparity!)entries only scored 401 points (huge disparity!)

-logically, because nice ones cooperate together, this is how TFT -logically, because nice ones cooperate together, this is how TFT wins! (though it cannot get a score higher than its opponent’s)wins! (though it cannot get a score higher than its opponent’s)

14 Entrants14 Entrants-3 countries, 5 disciplines (psychology, math, economics, sociology, -3 countries, 5 disciplines (psychology, math, economics, sociology,

political sciences)political sciences)

-scores range from 0 to 1000, but “useful benchmark for very good -scores range from 0 to 1000, but “useful benchmark for very good

performance is 600,” attained if both always cooperate togetherperformance is 600,” attained if both always cooperate together

-“very poor performance [benchmark] is 200 points” (if both always -“very poor performance [benchmark] is 200 points” (if both always D) D)

-winner Tit for Tat (TFT) scored 504 (but if change P=2, does not -winner Tit for Tat (TFT) scored 504 (but if change P=2, does not win)win)

-top 8 entries were nice (defined as not first to defect), rest were -top 8 entries were nice (defined as not first to defect), rest were notnot

-nice entries’ scores scored from 472 to 504, while best of mean -nice entries’ scores scored from 472 to 504, while best of mean entries only scored 401 points (huge disparity!)entries only scored 401 points (huge disparity!)

-logically, because nice ones cooperate together, this is how TFT -logically, because nice ones cooperate together, this is how TFT wins! (though it cannot get a score higher than its opponent’s)wins! (though it cannot get a score higher than its opponent’s)

14 Entrants14 Entrants-important to be nice and forgiving-important to be nice and forgiving

-2 kingmakers (defined as players who do not do well themselves -2 kingmakers (defined as players who do not do well themselves

but “LARGELY determine the rankings among the top contenders”): but “LARGELY determine the rankings among the top contenders”):

GRAASKAMP and DOWNINGGRAASKAMP and DOWNING

-DOWNING most important kingmaker since it had the largest range -DOWNING most important kingmaker since it had the largest range of scores achieved with the nice rules, important to note DOWNING of scores achieved with the nice rules, important to note DOWNING was not based on TFT principlewas not based on TFT principle

-now to look at the actual results!, then to examen the strategies, -now to look at the actual results!, then to examen the strategies, since strategies aside from TFT are just denoted by name of creatorsince strategies aside from TFT are just denoted by name of creator

14 Entrants14 Entrants-important to be nice and forgiving-important to be nice and forgiving

-2 kingmakers (defined as players who do not do well themselves -2 kingmakers (defined as players who do not do well themselves

but “LARGELY determine the rankings among the top contenders”): but “LARGELY determine the rankings among the top contenders”):

GRAASKAMP and DOWNINGGRAASKAMP and DOWNING

-DOWNING most important kingmaker since it had the largest range -DOWNING most important kingmaker since it had the largest range of scores achieved with the nice rules, important to note DOWNING of scores achieved with the nice rules, important to note DOWNING was not based on TFT principlewas not based on TFT principle

-now to look at the actual results!, then to examen the strategies, -now to look at the actual results!, then to examen the strategies, since strategies aside from TFT are just denoted by name of creatorsince strategies aside from TFT are just denoted by name of creator

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STRATEGIES!STRATEGIES!1. Tit for Tat (TFT)- winner with 504.5 points, from Toronto 1. Tit for Tat (TFT)- winner with 504.5 points, from Toronto

(psychology), as we all know- cooperates on first move, then does (psychology), as we all know- cooperates on first move, then does

what opponent did last move, “eye for eye” style, 4 lines FORTRANwhat opponent did last move, “eye for eye” style, 4 lines FORTRAN

2. TIDEMAN and CHIERUZZI- 500.4 points, from US (Economics), 2. TIDEMAN and CHIERUZZI- 500.4 points, from US (Economics),

begins with cooperation/ TFT, but after opponent finishes second begins with cooperation/ TFT, but after opponent finishes second

run of D, institutes extra punishment run of D, institutes extra punishment increases number of increases number of

punishments (D) by 1 with each run of opponent’s defections, then punishments (D) by 1 with each run of opponent’s defections, then

decides whether to give opponent a fresh start and begin with TFT decides whether to give opponent a fresh start and begin with TFT

again based on- if it has 10+ points more than opponent, opponent again based on- if it has 10+ points more than opponent, opponent

has not started another run of D’s, been 20+ moves since last fresh has not started another run of D’s, been 20+ moves since last fresh

start, are 10+ moves left, number of opponent’s D’s “differs from start, are 10+ moves left, number of opponent’s D’s “differs from

50-50 generator by at least 3 standard deviations,” 41 lines of code50-50 generator by at least 3 standard deviations,” 41 lines of code

STRATEGIES!STRATEGIES!1. Tit for Tat (TFT)- winner with 504.5 points, from Toronto 1. Tit for Tat (TFT)- winner with 504.5 points, from Toronto

(psychology), as we all know- cooperates on first move, then does (psychology), as we all know- cooperates on first move, then does

what opponent did last move, “eye for eye” style, 4 lines FORTRANwhat opponent did last move, “eye for eye” style, 4 lines FORTRAN

2. TIDEMAN and CHIERUZZI- 500.4 points, from US (Economics), 2. TIDEMAN and CHIERUZZI- 500.4 points, from US (Economics),

begins with cooperation/ TFT, but after opponent finishes second begins with cooperation/ TFT, but after opponent finishes second

run of D, institutes extra punishment run of D, institutes extra punishment increases number of increases number of

punishments (D) by 1 with each run of opponent’s defections, then punishments (D) by 1 with each run of opponent’s defections, then

decides whether to give opponent a fresh start and begin with TFT decides whether to give opponent a fresh start and begin with TFT

again based on- if it has 10+ points more than opponent, opponent again based on- if it has 10+ points more than opponent, opponent

has not started another run of D’s, been 20+ moves since last fresh has not started another run of D’s, been 20+ moves since last fresh

start, are 10+ moves left, number of opponent’s D’s “differs from start, are 10+ moves left, number of opponent’s D’s “differs from

50-50 generator by at least 3 standard deviations,” 41 lines of code50-50 generator by at least 3 standard deviations,” 41 lines of code

STRATEGIES!STRATEGIES!3. NYDEGGER- 485.5 points, starts with TFT for first 3 moves unless 3. NYDEGGER- 485.5 points, starts with TFT for first 3 moves unless it was only one to C on first move and only one to D on second it was only one to C on first move and only one to D on second move, then it will D on third move, after third move- it chooses move, then it will D on third move, after third move- it chooses based on a complex weighted sum (2 points for opponent’s D, 1 based on a complex weighted sum (2 points for opponent’s D, 1 point for own D, then weight this sum for past three terms- 16 for point for own D, then weight this sum for past three terms- 16 for last term, then 4, then 1; if sum = 63, i.e. three turns of mutual last term, then 4, then 1; if sum = 63, i.e. three turns of mutual defection defection it will C) it will C)

4. GROFMAN- 481.9 points, always cooperates unless players did 4. GROFMAN- 481.9 points, always cooperates unless players did not do the same thing on the last move, then cooperates with prob not do the same thing on the last move, then cooperates with prob 2/72/7

5. SHUBIK- 480.7 pts, cooperates until opponent plays D, then it 5. SHUBIK- 480.7 pts, cooperates until opponent plays D, then it defects once, if other defects again- it begins again with defects once, if other defects again- it begins again with cooperation, in general- “length of retaliation is increased by one for cooperation, in general- “length of retaliation is increased by one for each departure from mutual cooperation”each departure from mutual cooperation”

STRATEGIES!STRATEGIES!3. NYDEGGER- 485.5 points, starts with TFT for first 3 moves unless 3. NYDEGGER- 485.5 points, starts with TFT for first 3 moves unless it was only one to C on first move and only one to D on second it was only one to C on first move and only one to D on second move, then it will D on third move, after third move- it chooses move, then it will D on third move, after third move- it chooses based on a complex weighted sum (2 points for opponent’s D, 1 based on a complex weighted sum (2 points for opponent’s D, 1 point for own D, then weight this sum for past three terms- 16 for point for own D, then weight this sum for past three terms- 16 for last term, then 4, then 1; if sum = 63, i.e. three turns of mutual last term, then 4, then 1; if sum = 63, i.e. three turns of mutual defection defection it will C) it will C)

4. GROFMAN- 481.9 points, always cooperates unless players did 4. GROFMAN- 481.9 points, always cooperates unless players did not do the same thing on the last move, then cooperates with prob not do the same thing on the last move, then cooperates with prob 2/72/7

5. SHUBIK- 480.7 pts, cooperates until opponent plays D, then it 5. SHUBIK- 480.7 pts, cooperates until opponent plays D, then it defects once, if other defects again- it begins again with defects once, if other defects again- it begins again with cooperation, in general- “length of retaliation is increased by one for cooperation, in general- “length of retaliation is increased by one for each departure from mutual cooperation”each departure from mutual cooperation”

STRATEGIES!STRATEGIES!6. STEIN- 477.8 pts, TFT except it cooperates always first four 6. STEIN- 477.8 pts, TFT except it cooperates always first four moves and defects on last 2 moves (move 199 and 200 of game), moves and defects on last 2 moves (move 199 and 200 of game), every 15 moves checks to see if opponent is RANDOM with chi-every 15 moves checks to see if opponent is RANDOM with chi-squared test of opponent’s transition probabilities and alternating squared test of opponent’s transition probabilities and alternating CD/DC movesCD/DC moves

7. FRIEDMAN- 473.4 pts, cooperates until opponent defects, then it 7. FRIEDMAN- 473.4 pts, cooperates until opponent defects, then it defects foreverdefects forever

8. DAVIS- 471.9 pts, last of the nice guys, cooperates first 10 8. DAVIS- 471.9 pts, last of the nice guys, cooperates first 10 moves, then if there is a defection, it will defect forevermoves, then if there is a defection, it will defect forever

9. GRAASKAMP- 400.7 pts, one of kingmakers, TFT for 50 moves, 9. GRAASKAMP- 400.7 pts, one of kingmakers, TFT for 50 moves, defects on move 51, then plays 5 more TFT, check to see if defects on move 51, then plays 5 more TFT, check to see if opponent is RANDOM, if so- D from then on (also checks for TFT, opponent is RANDOM, if so- D from then on (also checks for TFT, ANALOGY, CLONE), otherwise- randomly defects every 5-15 moves, ANALOGY, CLONE), otherwise- randomly defects every 5-15 moves, enough trustenough trust

STRATEGIES!STRATEGIES!6. STEIN- 477.8 pts, TFT except it cooperates always first four 6. STEIN- 477.8 pts, TFT except it cooperates always first four moves and defects on last 2 moves (move 199 and 200 of game), moves and defects on last 2 moves (move 199 and 200 of game), every 15 moves checks to see if opponent is RANDOM with chi-every 15 moves checks to see if opponent is RANDOM with chi-squared test of opponent’s transition probabilities and alternating squared test of opponent’s transition probabilities and alternating CD/DC movesCD/DC moves

7. FRIEDMAN- 473.4 pts, cooperates until opponent defects, then it 7. FRIEDMAN- 473.4 pts, cooperates until opponent defects, then it defects foreverdefects forever

8. DAVIS- 471.9 pts, last of the nice guys, cooperates first 10 8. DAVIS- 471.9 pts, last of the nice guys, cooperates first 10 moves, then if there is a defection, it will defect forevermoves, then if there is a defection, it will defect forever

9. GRAASKAMP- 400.7 pts, one of kingmakers, TFT for 50 moves, 9. GRAASKAMP- 400.7 pts, one of kingmakers, TFT for 50 moves, defects on move 51, then plays 5 more TFT, check to see if defects on move 51, then plays 5 more TFT, check to see if opponent is RANDOM, if so- D from then on (also checks for TFT, opponent is RANDOM, if so- D from then on (also checks for TFT, ANALOGY, CLONE), otherwise- randomly defects every 5-15 moves, ANALOGY, CLONE), otherwise- randomly defects every 5-15 moves, enough trustenough trust

STRATEGIES!STRATEGIES!10. DOWNING- 390.6, main kingmaker, starts with D since assumes 10. DOWNING- 390.6, main kingmaker, starts with D since assumes opponent is unresponsive (i.e. initially assumes 1/2 for conditional opponent is unresponsive (i.e. initially assumes 1/2 for conditional probabilities, its downfall!), from then on- assesses and updates probabilities, its downfall!), from then on- assesses and updates probabilities (that opponent cooperates if DOWNING defects, etc) to probabilities (that opponent cooperates if DOWNING defects, etc) to calculate choice to maximize its long-term expected payoff, if the 2 calculate choice to maximize its long-term expected payoff, if the 2 conditional probabilities have similar values- DOWNING determines conditional probabilities have similar values- DOWNING determines pays to D, conversely- if opponent is responsive (much more likely pays to D, conversely- if opponent is responsive (much more likely to play C after DOWNING plays C than after D), then it will to play C after DOWNING plays C than after D), then it will cooperatecooperate

11. FELD- 327.6 pts, starts with TFT, gradually lowers probability of 11. FELD- 327.6 pts, starts with TFT, gradually lowers probability of C following the other plays C to 1/2 by the 200th moveC following the other plays C to 1/2 by the 200th move

12. JOSS- 304.4, cooperates 90% after opponent’s C, always D after 12. JOSS- 304.4, cooperates 90% after opponent’s C, always D after DD

13. TULLOCK- 300.5, cooperates first 11 moves, then cooperates 13. TULLOCK- 300.5, cooperates first 11 moves, then cooperates 10% less than opponent has on preceding 10 moves10% less than opponent has on preceding 10 moves

STRATEGIES!STRATEGIES!10. DOWNING- 390.6, main kingmaker, starts with D since assumes 10. DOWNING- 390.6, main kingmaker, starts with D since assumes opponent is unresponsive (i.e. initially assumes 1/2 for conditional opponent is unresponsive (i.e. initially assumes 1/2 for conditional probabilities, its downfall!), from then on- assesses and updates probabilities, its downfall!), from then on- assesses and updates probabilities (that opponent cooperates if DOWNING defects, etc) to probabilities (that opponent cooperates if DOWNING defects, etc) to calculate choice to maximize its long-term expected payoff, if the 2 calculate choice to maximize its long-term expected payoff, if the 2 conditional probabilities have similar values- DOWNING determines conditional probabilities have similar values- DOWNING determines pays to D, conversely- if opponent is responsive (much more likely pays to D, conversely- if opponent is responsive (much more likely to play C after DOWNING plays C than after D), then it will to play C after DOWNING plays C than after D), then it will cooperatecooperate

11. FELD- 327.6 pts, starts with TFT, gradually lowers probability of 11. FELD- 327.6 pts, starts with TFT, gradually lowers probability of C following the other plays C to 1/2 by the 200th moveC following the other plays C to 1/2 by the 200th move

12. JOSS- 304.4, cooperates 90% after opponent’s C, always D after 12. JOSS- 304.4, cooperates 90% after opponent’s C, always D after DD

13. TULLOCK- 300.5, cooperates first 11 moves, then cooperates 13. TULLOCK- 300.5, cooperates first 11 moves, then cooperates 10% less than opponent has on preceding 10 moves10% less than opponent has on preceding 10 moves

Last of STRATEGIES!Last of STRATEGIES!14. GRADUATE STUDENT NAME WITHHELD- 282.2 pts, starts with 14. GRADUATE STUDENT NAME WITHHELD- 282.2 pts, starts with

probability of C of 30%, which is updated every 10 moves if probability of C of 30%, which is updated every 10 moves if

opponent seems very cooperative, very uncooperative, or random, opponent seems very cooperative, very uncooperative, or random,

after 130 moves if losing- probability is adjusted, this complex after 130 moves if losing- probability is adjusted, this complex

process kept P between 30% and 70%, making it seem random to process kept P between 30% and 70%, making it seem random to

most opponentsmost opponents

15. RANDOM- 276.3 pts, C with probability 1/2 and D with 15. RANDOM- 276.3 pts, C with probability 1/2 and D with

probability 1/2 (C and D with equal probabilities)probability 1/2 (C and D with equal probabilities)

Last of STRATEGIES!Last of STRATEGIES!14. GRADUATE STUDENT NAME WITHHELD- 282.2 pts, starts with 14. GRADUATE STUDENT NAME WITHHELD- 282.2 pts, starts with

probability of C of 30%, which is updated every 10 moves if probability of C of 30%, which is updated every 10 moves if

opponent seems very cooperative, very uncooperative, or random, opponent seems very cooperative, very uncooperative, or random,

after 130 moves if losing- probability is adjusted, this complex after 130 moves if losing- probability is adjusted, this complex

process kept P between 30% and 70%, making it seem random to process kept P between 30% and 70%, making it seem random to

most opponentsmost opponents

15. RANDOM- 276.3 pts, C with probability 1/2 and D with 15. RANDOM- 276.3 pts, C with probability 1/2 and D with

probability 1/2 (C and D with equal probabilities)probability 1/2 (C and D with equal probabilities)

Tournament Num. 2 Tournament Num. 2 (1980)

-same non-zero sum setting, again round robin tournament (play -same non-zero sum setting, again round robin tournament (play

all)all)

-each entrant was sent report of first tournament, given same task-each entrant was sent report of first tournament, given same task

-instead of known number of moves per game, “length of the game -instead of known number of moves per game, “length of the game was determined probabilistically with .00346 chance of ending with was determined probabilistically with .00346 chance of ending with each given move” (one way to include each given move” (one way to include ww), ), ww chosen so expected chosen so expected median length = 200 moves (median length = 200 moves (ww = .99654 in second tournament) = .99654 in second tournament)

-average length turned out to be shorter: closer to 150 moves-average length turned out to be shorter: closer to 150 moves

-endgame effects successfully avoided this time-endgame effects successfully avoided this time

-features of entries do not relate to success (length of program, -features of entries do not relate to success (length of program, type, nationality, type of program, etc)type, nationality, type of program, etc)

Tournament Num. 2 Tournament Num. 2 (1980)

-same non-zero sum setting, again round robin tournament (play -same non-zero sum setting, again round robin tournament (play

all)all)

-each entrant was sent report of first tournament, given same task-each entrant was sent report of first tournament, given same task

-instead of known number of moves per game, “length of the game -instead of known number of moves per game, “length of the game was determined probabilistically with .00346 chance of ending with was determined probabilistically with .00346 chance of ending with each given move” (one way to include each given move” (one way to include ww), ), ww chosen so expected chosen so expected median length = 200 moves (median length = 200 moves (ww = .99654 in second tournament) = .99654 in second tournament)

-average length turned out to be shorter: closer to 150 moves-average length turned out to be shorter: closer to 150 moves

-endgame effects successfully avoided this time-endgame effects successfully avoided this time

-features of entries do not relate to success (length of program, -features of entries do not relate to success (length of program, type, nationality, type of program, etc)type, nationality, type of program, etc)

63 Entrants63 Entrants-6 countries, contests largely recruited via journals, etc-6 countries, contests largely recruited via journals, etc

-everyone from first tournament re-invited, entrants ranged from 11 -everyone from first tournament re-invited, entrants ranged from 11 year-old Steve Newman to professors from many disciplines, year-old Steve Newman to professors from many disciplines, including computer science and evolutionary biology this timeincluding computer science and evolutionary biology this time

-more than half of entries were nice, Tit for Tat (TFT) won again -more than half of entries were nice, Tit for Tat (TFT) won again

-Tit for Two Tats- too forgiving, suggested post-Tourney 1, -Tit for Two Tats- too forgiving, suggested post-Tourney 1, submitted Tourney 2 by evolutionary biologist, ended up in bottom submitted Tourney 2 by evolutionary biologist, ended up in bottom half of grouphalf of group

-5 representative rules can predict how a given rule did with the 63 -5 representative rules can predict how a given rule did with the 63 rules- GRAASKAMP & KATZEN (Srules- GRAASKAMP & KATZEN (S66), PINKLEY (S), PINKLEY (S3030), ADAMS (S), ADAMS (S3535), ), GLADSTEIN (SGLADSTEIN (S4646), and FEATHERS (S), and FEATHERS (S2727) ) predicted tournament score predicted tournament score T = 120 + (.202) ST = 120 + (.202) S6 6 + (.198) S+ (.198) S3030 + (.110) S + (.110) S3535 + (.072) S + (.072) S4646 + (.086) S + (.086) S2727

63 Entrants63 Entrants-6 countries, contests largely recruited via journals, etc-6 countries, contests largely recruited via journals, etc

-everyone from first tournament re-invited, entrants ranged from 11 -everyone from first tournament re-invited, entrants ranged from 11 year-old Steve Newman to professors from many disciplines, year-old Steve Newman to professors from many disciplines, including computer science and evolutionary biology this timeincluding computer science and evolutionary biology this time

-more than half of entries were nice, Tit for Tat (TFT) won again -more than half of entries were nice, Tit for Tat (TFT) won again

-Tit for Two Tats- too forgiving, suggested post-Tourney 1, -Tit for Two Tats- too forgiving, suggested post-Tourney 1, submitted Tourney 2 by evolutionary biologist, ended up in bottom submitted Tourney 2 by evolutionary biologist, ended up in bottom half of grouphalf of group

-5 representative rules can predict how a given rule did with the 63 -5 representative rules can predict how a given rule did with the 63 rules- GRAASKAMP & KATZEN (Srules- GRAASKAMP & KATZEN (S66), PINKLEY (S), PINKLEY (S3030), ADAMS (S), ADAMS (S3535), ), GLADSTEIN (SGLADSTEIN (S4646), and FEATHERS (S), and FEATHERS (S2727) ) predicted tournament score predicted tournament score T = 120 + (.202) ST = 120 + (.202) S6 6 + (.198) S+ (.198) S3030 + (.110) S + (.110) S3535 + (.072) S + (.072) S4646 + (.086) S + (.086) S2727

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