# Party competition Ch7

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### WHAT IS IT?

This implements the evolutionary model of party competition, with endogenous party birth and death, specified in Chapter 7 of Michael Laver and Ernest Sergenti's book, Party competition: an agent based model (Princeton University Press, 2012). A full description and analysis of the model can be found in this book and is not repeated here.

Party positions and voter ideal points are defined in two dimensions of policy/ideology, directly analogous to the dimensions used in other "spatial" models of political competition. The horizontal dimension might, for example, be seen as describing left-right economic policy positions; the vertical dimension might be seen as a liberal-conservative policy dimension on matters such as abortion, sexual orientation, euthanasia.

VOTERS always vote for the closest party. The preference structure of the voting population can be designed as if this is an aggregate of up to three subpopulations. (Only two are investigated by Laver and Sergenti and the default setting on the interface sets the size of the third subpopulation at zero). Voters in each subpopulation have normally distributed ideal points, and each subpopulation is characterized by: the number of voters it comprises; the standard deviation of the distribution of its voters' ideal points, and the means of this distribution on the x and y dimensions. All of these parameters can be set using the sliders in the _Population Designer_ panel near the bottom of the interface. Alternatively, the _random population_ button picks these at random.

PARTY LEADERS compete with each other by offering policies to potential supporters. They use one of five parameterized _species_ of decision rule to select a party policy position. The species are: Sticker, Aggregator, Hunter, Predator and Exporer. Rule parameters control speed of adaptation (speed), comfort threshold (kappa) and exploration neighborhood (eta). These rules and parameters are described fully in Laver and Sergenti (2012) and implemented in the _party dynamics_ section of the code.

DYNAMICS OF PARTY COMPETITION. The baseline dynamics of the model iterate forever. (1) Voters support their closest party. (2) Given a profile of voter support for parties, leaders adapt party policy positions using their decision rule. (3) Go to 1.

The set of surviving political parties is fully endogenous to the model.

EXISTING PARTIES DIE if their updated fitness, denominated in vote share, falls below a system survival threshold. The party survival threshold, and the memory parameter in the fitness updating regime, can be set using the sliders in the _Environment_ panel near the top of the interface.

NEW PARTIES ARE BORN at the ideal points of disgruntled voters and are allocated a parameterized decision rule at random. Parameters of the party birth regime can be set using the sliders in the _Party birth_ panel near the top of the interface. There is a switch on the interface that turns off endogenous party birth and instead randomly generates new party births at random locations. (This was not investigated systematically by Laver and Sergenti.)

Model ticks are divided into CAMPAIGN TICKS and ELECTION TICKS. Party leaders adapt their positions during campaign ticks but receive no rewards or punishments. Parties can only die or be born on election ticks. The number of campaign ticks per election tick can be set using the slider in the _Environment_ panel near the top of the interface.

### HOW TO USE IT

The set of available decision rules, and the set of avaialble parameterizations of these rules, are hard coded in the "set-rule-list" procedure in the setup routine. (This is obviously less than elegant and it would be better to load this list from a file). Comments below this procedure explain the coding of a given rule parameterization, which is equivalent to a party leader's "decision-making DNA". Some parameters are redundant for some rules (all are redundant for Sticker, for example). The research design of the Laver-Sergenti experiments requires that all rule SPECIES have an equal chance of random selection, and "clones" of Sticker and Aggregator rules, all with the same parameterization, are included to enable this. The current, easily editable, rule list is the one used for the experiment reported in Chapter 7 of Laver and Sergenti.

SETUP sets up parties, supporters and system parameters as specified above. GO starts and stops the simulation using current parameters.

(Hitting SETUP while GO is still pressed very occasionally causes an error depending where precisely the program is when setup is hit; this easily retrieved by unpressing GO and pressing SETUP again.)

RUNNING EXPERIMENTS. Laver and Sergenti designed a large computational experiment, and report results of this, in Chapter 7 of their book. Although the _production_ run was executed on a high performance cluster, precisely equivalent smaller scale experiments can easily be run using Behavior Space. Sketch runs for all results reported in Laver and Sergenti were generated using Behavior Space on a normal laptop. Some sample behavior space experiments are included.

DATA OUTPUT. Standard data output is via Behavior Space experiments used in the normal way. There is a separate data channel that writes out information on party births and deaths only when these occur. This is activated by a switch and a file name on the interface.

### WHAT TO PLAY WITH

The most obvious new source of potential experimentation concerns rule parameterizations. These can easily be changed by editing the rule-list in the setup procedure. Any number of parametizations can enter this list, which can be as large and varied as you like. The larger the rule list, however, the longer it will take to "map out" the steady state distribution of model outputs. The less systematically it is constructed, the harder it will be to make sense of model outputs.

Laver and Sergenti report results from a carefully controlled computational experiment and only investigate electorate with two subpopulations. There are infinitely many alternative populations for you to explore using the population designer. There are also many parameterizations of the competitive environment, and the party birth regime, not explored by Laver and Sergenti. You may, for example, want to specify a parameterization of the model you feel corresponds to some real political system that interests you.

By far the most exciting and callenging way forward is to specify and program your own decision rule for party leaders. Just drop in your coded new rule as a procedure in the party dynamics section, add its name to the rule list, edit it in to the _adapt_ and _color-myself_ procedures, and add a reporter for your rule_s vote share to the interface. You_re good to go!

### CREDITS AND REFERENCES

Programmed by:

Michael Laver, Department of Politics, New York University

ml127@nyu.edu

Ernest Sergenti, The World Bank

esergenti@gmail.com

## Comments and Questions

;;____________________________ ; ;; SETUP AND HOUSEKEEPING ;;____________________________ breed [ parties party ] globals [ total-votes max-voteshare ; largest vote share on any patch mean-voterx ; mean voter x-coordinate mean-votery ; mean voter y-coordinate cycle election ; election number mean-eccentricity ; mean Euclidean distance of parties from (mean-voterx, mean-votery) voter-misery ; mean quadratic Euclidean voter distance from closest party enp ; effective number of parties = 1/(sum of squared party vote shares) enr ; effective number of rules = 1/(sum of squared rule vote shares) rule-number ; rule number rule-list ; list of available decision rules rule-voteshare ; list of vote shares won by the set of parties using each rule rule-pcount ; number of parties using rule rule-eccent ; mean eccentricity of parties using rule ] parties-own [ rule ; party's parameterized decision rule species ; party's decision rule species ; decision rule parameters speed ; distance each party moves per tick comfort-kappa ; comfort threshold - implement rule iff fitness below this neighborhood-eta ; radius from party postion of local neighborhood ; indicators mysize ; current party size old-size ; party's size previous tick old-x ; x-coordinate of my position at previous election old-y ; y-coordinate of my position at previous election age ; number of elections survived since birth fitness ; party's evolutionary fitness eccentricity ; party's Euclidean distance from (mean-voterx, mean-votery) ; rule-specific variables prey ; for predators: party I am thinking of attacking best-x ; for explorers: explored x-coordinate with highest vote share during campaign best-y ; for explorers: explored y-coordinate with highest vote share during campaign best-size ; for explorers: highest vote share of party during campaign ] patches-own [ votes ; number of voters on patch vote-share ; proportion of total voters on patch closest-party ; party with smallest Euclidean distance from patch misery ; quadratic distance from closest party, weighted by patch's vote share ] to setup clear-all file-close if (endogenous-birth = false) [set misery-alpha 0 set misery-beta 0] if (birth-death-file = true) [ if (file-exists? bd-file-name) [file-delete bd-file-name] file-open bd-file-name ] set rule-list (list "S00000000a" "S00000000h" "S00000000o" "S00000000v" "S00000000ac" "S00000000b" "S00000000i" "S00000000p" "S00000000w" "S00000000ad" "S00000000c" "S00000000j" "S00000000q" "S00000000x" "S00000000ae" "S00000000d" "S00000000k" "S00000000r" "S00000000y" "S00000000af" "S00000000e" "S00000000l" "S00000000s" "S00000000z" "S00000000ag" "S00000000f" "S00000000m" "S00000000t" "S00000000aa" "S00000000ah" "S00000000g" "S00000000n" "S00000000u" "S00000000ab" "S00000000ai" "A02500000a" "A05000000a" "A10000000a" "A20000000a" "A40000000a" "A02500000b" "A05000000b" "A10000000b" "A20000000b" "A40000000b" "A02500000c" "A05000000c" "A10000000c" "A20000000c" "A40000000c" "A02500000d" "A05000000d" "A10000000d" "A20000000d" "A40000000d" "A02500000e" "A05000000e" "A10000000e" "A20000000e" "A40000000e" "A02500000f" "A05000000f" "A10000000f" "A20000000f" "A40000000f" "A02500000g" "A05000000g" "A10000000g" "A20000000g" "A40000000g" "H02500600" "H05000600" "H10000600" "H20000600" "H40000600" "H02501100" "H05001100" "H10001100" "H20001100" "H40001100" "H02501600" "H05001600" "H10001600" "H20001600" "H40001600" "H02502100" "H05002100" "H10002100" "H20002100" "H40002100" "H02502600" "H05002600" "H10002600" "H20002600" "H40002600" "H02503100" "H05003100" "H10003100" "H20003100" "H40003100" "H02510000" "H05010000" "H10010000" "H20010000" "H40010000" "P02500600" "P05000600" "P10000600" "P20000600" "P40000600" "P02501100" "P05001100" "P10001100" "P20001100" "P40001100" "P02501600" "P05001600" "P10001600" "P20001600" "P40001600" "P02502100" "P05002100" "P10002100" "P20002100" "P40002100" "P02502600" "P05002600" "P10002600" "P20002600" "P40002600" "P02503100" "P05003100" "P10003100" "P20003100" "P40003100" "P02510000" "P05010000" "P10010000" "P20010000" "P40010000" "E00000602" "E00000604" "E00000606" "E00000608" "E00000610" "E00001102" "E00001104" "E00001106" "E00001108" "E00001110" "E00001602" "E00001604" "E00001606" "E00001608" "E00001610" "E00002102" "E00002104" "E00002106" "E00002108" "E00002110" "E00002602" "E00002604" "E00002606" "E00002608" "E00002610" "E00003102" "E00003104" "E00003106" "E00003108" "E00003110" "E00010002" "E00010004" "E00010006" "E00010008" "E00010010" ) ;; the 10-character rule names store the parameterization (genetic code) of each rule, as follows: ;; character 1 = rule species; chars 2-4 = speed (step size); chars 5-7 = comfort kappa; chars 8-9 = neighborhood eta ;; for example, H02501200 is a Hunter with speed = 0.25, kappa = 0.12 and eta = 0.00 ;; (though eta is redundant for Hunters) ;; and E00010050 is an Explorer with speed = 0.00, kappa = 1.00 and eta = 0.50 ;; (though speed is redundant for Explorers) set rule-number n-values length(rule-list) [?] set rule-voteshare n-values length(rule-list) [0] set rule-pcount n-values length(rule-list) [0] set rule-eccent n-values length(rule-list) [-1] create-parties 1 ask parties [set fitness 1 set heading random-float 360 jump random-float 30 set old-x xcor set old-y ycor set age 0 set size 2 random-pick load-rule-parameters color-myself ] ;; every run starts with a single party, which has a random position and rule picked from the rule list ask patches [ let x1 (pxcor - x-mean1) / sd-1 let y1 (pycor - y-mean1) / sd-1 set votes votes1 * exp (-0.5 * ( x1 ^ 2 + y1 ^ 2)) / (2 * pi * sd-1 ^ 2) ;; votes1, x_mean1, y_mean1, sd_1 = votes, mean and standard deviation of subpopulation 1, read from interface ;; each patch's votes arising from subpopulation 1 = votes1 * bivariate normal density with mean1, sd_1, rho = 0 if (votes2 > 0)[ let x2 (pxcor - x-mean2) / sd-2 let y2 (pycor - y-mean2) / sd-2 set votes votes + votes2 * exp (-0.5 * ( x2 ^ 2 + y2 ^ 2)) / (2 * pi * sd-2 ^ 2)] ;; add votes to each patch from subpopulation 2, calculated as above if (votes3 > 0)[ let x3 (pxcor - x-mean3) / sd-3 let y3 (pycor - y-mean3) / sd-3 set votes votes + votes3 * exp (-0.5 * ( x3 ^ 2 + y3 ^ 2)) / (2 * pi * sd-3 ^ 2)] ;; add votes to each patch from subpopulation 3, calculated as above ] set total-votes sum [ votes ] of patches type "Total votes at all locations = " type round(total-votes) ;; add total of votes on all patches and output this to the command window ask patches [set vote-share votes / total-votes] ;calculate each patch's vote share set mean-voterx sum [ pxcor * vote-share ] of patches set mean-votery sum [ pycor * vote-share ] of patches type " Mean voter x = " type round(mean-voterx) type " Mean voter y = " print round(mean-votery) ;; calculate center (mean) of voter distribution on each dimension as sum of (patch positions weighted by vote share) ;; output this to the command window set max-voteshare max [ vote-share ] of patches ask patches [set pcolor scale-color gray vote-share 0 max-voteshare ] ;; color patches red with density proportional to vote shares update-support ;; ask voters to choose closest party and calculate relative success of different rules update-rule-measures end ; ******* parameter setup buttons to random-pop set sd-1 5 set sd-2 5 set y-mean1 0 set y-mean2 0 set x-mean2 precision (random-float 15) 2 set x-mean1 0 - x-mean2 set votes1 500000 + random 166667 set votes2 1000000 - votes1 end ;;____________________________ ; ;; PARTY DYNAMICS ;;____________________________ to stick ;; do nothing end to aggregate if (mysize > 0) [ let xbar (sum [votes * pxcor] of patches with [closest-party = myself] / mysize) let ybar (sum [votes * pycor] of patches with [closest-party = myself] / mysize) let dist distancexy xbar ybar facexy xbar ybar ifelse (dist >= speed) [jump speed] [setxy xbar ybar] ] ;; identify xbar, ybar, the mean x, y positions of current party members ;; if you will not overshoot (xbar, ybar) face this and jump distance "speed" towards (xbar, ybar) ;; maintain current position if zero supporters end to hunt ifelse (mysize > old-size) [jump speed] [set heading heading + 90 + random-float 180 jump speed] ;; hunter makes a move of size speed in same direction as previous move if this increased party support ;; else reverses direction and makes a move of size speed in on a heading chosen from the 180 degree arc now faced set old-size mysize ;; remember party size for next cycle end to sat-hunt ifelse (mysize / total-votes < comfort-kappa) [hunt] [stick] end ;; hunt if vote share is below comfort-kappa, else stand still to predate let me mysize set prey min-one-of other parties with [mysize > me] [distance myself] ;; find the closest larger party if prey != nobody [ let xdest [xcor] of prey let ydest [ycor] of prey facexy xdest ydest let dist distancexy xdest ydest ifelse (dist >= speed) [jump speed] [setxy xdest ydest] ;; if you will not overshoot (xdest, ydest), jump "speed" towards this ] end to sat-predate ifelse (mysize / total-votes < comfort-kappa) [predate] [stick] end ;; predate if vote share is below comfort-kappa, else stand still to explore if (mysize > best-size) [set best-x xcor set best-y ycor set best-size mysize] ;; NB voter support is updated AFTER all party adaptation is finished ;; so the effect on party support of a move made the previous tick is assessed BEFORE adaptation this tick ;; if you found a position with more support than your previous best-size, update your best position ifelse (remainder cycle campaign-ticks != 0) [setxy old-x old-y set heading random-float 360 jump random-float neighborhood-eta] ;; if there is no election, test a random position within eta of your position at the last election [if (best-size > old-size) [setxy best-x best-y] ;; if there is an election, go to a better postion iff you have found one set best-size 0] ;;after the election zero best-size, which stores the best size found in inter-electoral exploration ;;NB in update-party-measures, all parties update old-x, old-y and old-size after each election end ;; Each NON-ELECTION tick, explorer tests random positions "close" to its position at the last election. ;; "Close" is defined by neighborhood-eta, the maximum number of patches a party can move between elections. ;; During exploration, Explorer updates best-x, best-y, best-size iff tested co-ordinates ;; generate more support than the previous best-xy co-ordinates ;; Each ELECTION tick, explorer sets its position as the best location found in inter-electoral exploration, ;; Provided this yields more support than the previous electoral position to sat-explore ifelse (mysize / total-votes < comfort-kappa) [explore] [stick] end ;; explore if vote share is below its comfort-kappa, else stand still ;;____________________________ ;; ;; MAIN CONTROL SUBROUTINES ;;____________________________ to update-support ask patches [set closest-party min-one-of parties [distance myself]] ;; patches find their closest party ask parties [set mysize sum [votes] of patches with [closest-party = myself]] ;; each party sums the votes on patches for which it is the closest party end to calculate-election-results set election election + 1 update-party-measures update-rule-measures measure-enp measure-enr measure-eccentricity measure-misery party-death party-birth end to update-party-measures ask parties [ set fitness fitness-alpha * fitness + (1 - fitness-alpha) * mysize / total-votes ;; parties recursively update their fitness as: (alpha)*(previous fitness) + (1-alpha)*(current vote share) set age age + 1 set old-x xcor set old-y ycor ] end to update-rule-measures (foreach rule-number rule-list [ set rule-voteshare replace-item ?1 rule-voteshare sum [mysize / total-votes] of parties with [rule = ?2] ;; calculate the current support level of all parties using each rule set rule-pcount replace-item ?1 rule-pcount count parties with [rule = ?2] ;; count the number of parties using each rule ifelse (sum [mysize] of parties with [rule = ?2] > 0) [ set rule-eccent replace-item ?1 rule-eccent mean [eccentricity] of parties with [rule = ?2] ] ;;calculate the mean of eccentricity, policy loss and policy shift of all parties using each rule [ set rule-eccent replace-item ?1 rule-eccent -1 ] ;;these measures have no meaning when no party uses a rule ]) end to measure-enp set enp (total-votes ^ 2) / (sum [mysize ^ 2] of parties) ;; calculate the enp of the system end to measure-enr let stick-var ( sum(sublist rule-voteshare 0 35) ) ^ 2 let agg1-var ( sum(sublist rule-voteshare 35 36) + sum(sublist rule-voteshare 40 41) + sum(sublist rule-voteshare 45 46) + sum(sublist rule-voteshare 50 51) + sum(sublist rule-voteshare 55 56) + sum(sublist rule-voteshare 60 61) + sum(sublist rule-voteshare 65 66) ) ^ 2 let agg2-var ( sum(sublist rule-voteshare 36 37) + sum(sublist rule-voteshare 41 42) + sum(sublist rule-voteshare 46 47) + sum(sublist rule-voteshare 51 52) + sum(sublist rule-voteshare 56 57) + sum(sublist rule-voteshare 61 62) + sum(sublist rule-voteshare 66 67) ) ^ 2 let agg3-var ( sum(sublist rule-voteshare 37 38) + sum(sublist rule-voteshare 42 43) + sum(sublist rule-voteshare 47 48) + sum(sublist rule-voteshare 52 53) + sum(sublist rule-voteshare 57 58) + sum(sublist rule-voteshare 62 63) + sum(sublist rule-voteshare 67 68) ) ^ 2 let agg4-var ( sum(sublist rule-voteshare 38 39) + sum(sublist rule-voteshare 43 44) + sum(sublist rule-voteshare 48 49) + sum(sublist rule-voteshare 53 54) + sum(sublist rule-voteshare 58 59) + sum(sublist rule-voteshare 63 64) + sum(sublist rule-voteshare 68 69) ) ^ 2 let agg5-var ( sum(sublist rule-voteshare 39 40) + sum(sublist rule-voteshare 44 45) + sum(sublist rule-voteshare 49 50) + sum(sublist rule-voteshare 54 55) + sum(sublist rule-voteshare 59 60) + sum(sublist rule-voteshare 64 65) + sum(sublist rule-voteshare 69 70) ) ^ 2 let den stick-var + agg1-var + agg2-var + agg3-var + agg4-var + agg5-var let other-rules sublist rule-voteshare 70 175 foreach other-rules [ set den den + (? * ?) ] ifelse (den <= 0) [ set enr 0 ] [set enr 1 / den ] ;; calculate the effective-number-of-rules of the system end to measure-eccentricity ask parties [set eccentricity sqrt ((xcor - mean-voterx) ^ 2 + (ycor - mean-votery) ^ 2) / 10] ;; calculate each party's eccentricity, its Euclidean distance from the center of the voter distribution set mean-eccentricity mean [eccentricity] of parties ;; calculate the mean eccentricity of all parties in the system end to measure-misery ask patches [set misery misery-alpha * misery + (1 - misery-alpha) * ((distance closest-party ^ 2) / 100) * vote-share] set voter-misery sum [misery] of patches ;; patch misery is misery at t-1, updated by mean quadratic Euclidean distance of patch from closest party, ;; weighted by patch vote share ;; mean voter "misery" is thus updated mean quadratic Euclidean distance of each voter from his/her closest party end to party-death ask parties [if (fitness < survival-threshold and count parties > 2) [ if (birth-death-file = true) [ file-write votes1 file-write x-mean1 file-write votes2 file-write x-mean2 file-write fitness-alpha file-write survival-threshold file-write campaign-ticks file-write misery-alpha file-write misery-beta file-write election file-write "death" file-write rule file-write who file-write precision xcor 4 file-write precision ycor 4 file-write "age" file-write age file-print "" ] die ask patches [set closest-party min-one-of parties [distance myself]] ]] ;; parties whose updated fitness falls below the survival threshold write out their data and die ;; as long as there are at least two parties end to party-birth ifelse (endogenous-birth = true) [ ask one-of patches with [distancexy 0 0 < 30] [ if (random-float 1 < (misery-beta * misery * 1000)) [sprout-parties 1 [initialize-party] ]]] ;; pick a random patch within three standard deviations of the origin. ;; the probability this patch sprouts a new party is proportional to (misery-beta)*(patch misery) ;; the greater patch misery, the higher the probability the patch sprouts a new party. ;; NB patch misery is scaled, in measure-misery above, to the share of all voters on the patch, ;; this share maxes at 0.00159 for the (0,0) patch in a unimodal (0,10) distribution and is 0.0002 at patch (20,0) in this distibution ;; this explains the scaling up of the patch misery score by 1000 and the units of beta are thus sui generis to the simulation ;; the greater beta, however, the more sensitive are voters on a patch to a given level of misery. ;; new-born parties intially locate at the position of the "sprouting" patch. [ create-parties 1 [set heading random-float 360 jump random-float 30 initialize-party] ] ;; non-endogenous initial party locations take a random walk within 30 from the origin end to initialize-party ifelse (count parties = 0) [set fitness 1] [set fitness 1 / count parties] set heading random-float 360 set old-x xcor set old-y ycor set age 0 set size 1.5 random-pick load-rule-parameters color-myself if (birth-death-file = true) [ file-write votes1 file-write x-mean1 file-write votes2 file-write x-mean2 file-write fitness-alpha file-write survival-threshold file-write campaign-ticks file-write misery-alpha file-write misery-beta file-write election file-write "birth" file-write rule file-write who file-write precision xcor 4 file-write precision ycor 4 file-print "" ] ;;Write out your starting data before handing control back to the observer end to random-pick set rule one-of rule-list ;; randomly pick a rule from the rule list end to load-rule-parameters ; set parameters of your decision rule by reading the relevant parts of your rule name set species first rule set speed (read-from-string substring rule 1 4) / 100 set comfort-kappa (read-from-string substring rule 4 7) / 100 set neighborhood-eta (read-from-string substring rule 7 9) end to color-myself if (species = "S") [set color yellow] if (species = "A") [set color lime] if (species = "H") [set color violet] if (species = "P") [set color red] if (species = "E") [set color blue] end to adapt if (species = "S") [stick] if (species = "A") [aggregate] if (species = "H") [sat-hunt] if (species = "P") [sat-predate] if (species = "E") [sat-explore] end ;;____________________________ ; ;; MAIN CONTROL ROUTINE ;;____________________________ to go repeat campaign-ticks [ set cycle cycle + 1 ask parties [adapt] update-support if (remainder cycle campaign-ticks = 0 and cycle != 0) [calculate-election-results] ] end

There is only one version of this model, created over 11 years ago by Michael Laver.

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