# Party competition Ch6

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### WHAT IS IT?

This implements the model of party competition, with endogenous party birth and death, specified in Chapter 6 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 a liberal-conservative policy dimension on matters such as abortion, sexuality, 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 (though 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 three _species_ of decision rule _ Sticker, Aggregator, Hunter _ to select a party policy position. These riles are specified 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 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. 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

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 6 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.

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

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 ; cycle (or campaign) number or tick election ; election number or tick 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) 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 ; decision rule parameters speed ; distance each party moves per tick ; 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) ] 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 the endogenous-birth option has not been chosen, set misery-alpha and misery-beta to 0 if (birth-death-file = true) [ if (file-exists? bd-file-name) [file-delete bd-file-name] file-open bd-file-name ; if a birth-death file has been requested, delete any previous birth-death files with name equal to bd-file-name and ; open a new file with name equal to bd-file-name. ] set rule-list (list "sticker" "aggregator" "hunter") 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] ; initialize rule measure vectors: rule-list is the vector of all of rules examined; rule-number is a unique number for each ; rule; rule-voteshare and rule-pcount are initialized at 0 for each rule; and rule-eccent is initialized at -1 for each rule 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 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 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 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 red 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 ;; update rule-measure vectors 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 to symmetric-pop set sd-1 10 set x-mean1 0 set y-mean1 0 set votes1 1000000 set votes2 0 set votes3 0 set x-mean2 0 end ;;____________________________ ; ;; PARTY DYNAMICS ;;____________________________ to stick ;; do nothing end to aggregate if (mysize > 0) [ set xcor (sum [votes * pxcor] of patches with [closest-party = myself] / mysize) set ycor (sum [votes * pycor] of patches with [closest-party = myself] / mysize) ] ;; set party x, y positions at the mean x, y positions of party members; 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 ;;____________________________ ;; ;; 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-eccentricity measure-misery party-death party-birth end ; execute the above set of commands at every election tick 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-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 speed 1 set age 0 set size 1.5 random-pick 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 "" ] ;; initialize a new party by picking a random rule from the rule list and ;; 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 list in the setup routine end to color-myself if (rule = "sticker") [set color yellow] if (rule = "aggregator") [set color lime] if (rule = "hunter") [set color violet] end to adapt if (rule = "sticker") [stick] if (rule = "aggregator") [aggregate] if (rule = "hunter") [hunt] ;; NB stickers do nothing end ;;____________________________ ; ;; MAIN CONTROL ROUTINE ;;____________________________ to go repeat campaign-ticks ; for each election, repeat the following commands [campaign-ticks] times [ set cycle cycle + 1 ask parties [adapt] update-support if (remainder cycle campaign-ticks = 0 and cycle != 0) [calculate-election-results] ; increase the cycle number; ask parties to adapt using their rules; update party support; ; and if the remainder of the cycle number divided by campaign ticks is zero, calculate election results ] end

There is only one version of this model, created almost 7 years ago by Michael Laver.

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