Bail​ ​Bloc​ ​Simulation

When​ ​developing​ ​Bail​ ​Bloc,​ ​it​ ​became​ ​vital​ ​to​ ​communicate​ ​the​ ​potential​ ​impact.
Given​ ​a​ ​number​ ​of​ ​participants​ ​("miners")​ ​and​ ​period​ ​of​ ​months,​ ​this​ ​simulation​ ​estimates​ ​Bail
Bloc's​ ​impact​ ​in​ ​terms​ ​of​ ​the​ ​accumulated​ ​bail​ ​fund​ ​and​ ​how​ ​many​ ​people​ ​this​ ​can​ ​release​ ​frompretrial​ ​detention.

Data
The​ ​data​ ​for​ ​this​ ​simulation​ ​were​ ​collected​ ​in​ ​part​ ​from​ ​the​ ​Bronx​ ​Freedom​ ​Fund's​ ​own​ ​statistics
and​ ​[1],​ ​but​ ​primarily​ ​from​ ​[2].
In​ ​detail,​ ​the​ ​data​ ​used​ ​are​ ​(unless​ ​otherwise​ ​noted,​ ​these​ ​are​ ​all​ ​NYC-specific):● A​ ​distribution​ ​of​ ​bail​ ​amounts​ ​less​ ​than​ ​or​ ​equal​ ​to​ ​$10,000(Figure​ ​9,​ ​p47​ ​of​ ​[1]).
○ In​ ​the​ ​paper​ ​these​ ​data​ ​are​ ​pre-bucketed;​ ​in​ ​lieu​ ​of​ ​individual​ ​information​ ​weassume​ ​that​ ​bails​ ​are​ ​uniformly​ ​distributed​ ​within​ ​these​ ​buckets.
○ The​ ​paper​ ​includes​ ​bail​ ​amounts​ ​above​ ​$10,000.​ ​This​ ​accounts​ ​for​ ​less​ ​than​ ​1%of​ ​the​ ​population​ ​which​ ​we​ ​omitted,​ ​assuming​ ​our​ ​funds​ ​will​ ​be​ ​used​ ​for​ ​smaller
amounts​ ​of​ ​bail.
● A​ ​distribution​ ​of​ ​what​ ​percentage​ ​within​ ​a​ ​bail​ ​bucket​ ​successfully​ ​makes​ ​bail​ ​(Table​ ​7,p51​ ​of​ ​[1]).
○ Bail​ ​amounts​ ​in​ ​the​ ​bucket​ ​[1,​ ​25]​ ​are​ ​not​ ​included;​ ​we​ ​assume​ ​that​ ​100%​ ​of​ ​bailin​ ​that​ ​bucket​ ​is​ ​made.
● A​ ​distribution​ ​of​ ​pretrial​ ​detention​ ​durations,​ ​in​ ​days​ ​(Figure​ ​45,.p121​ ​of​ ​[1]).​ ​There​ ​is​ ​noupper-bound​ ​described,​ ​so​ ​it​ ​is​ ​arbitrarily​ ​set​ ​as​ ​200.
● Adjusted​ ​"failure​ ​to​ ​appear"​ ​(FTA)​ ​rate​ ​(Figure​ ​35,​ ​p96​ ​of​ ​[1]).

Simulation​ ​DesignThe​ ​simulation​ ​time​ ​interval​ ​is​ ​measured​ ​in​ ​months.
Each​ ​month,​ ​we​ ​sample​ ​a​ ​bail​ ​population​ ​based​ ​on​ ​the​ ​data​ ​above.​ ​This​ ​includes:​ ​bail​ ​amount,whether​ ​or​ ​not​ ​they​ ​pay​ ​it​ ​on​ ​their​ ​own,​ ​how​ ​long​ ​they​ ​will​ ​be​ ​detained​ ​for,​ ​and​ ​whether​ ​or​ ​notthey​ ​will​ ​plead​ ​guilty​ ​(which​ ​could​ ​but​ ​doesn't​ ​necessarily​ ​indicate​ ​a​ ​plea​ ​deal).
We​ ​also​ ​compute​ ​a​ ​new​ ​XMR-to-USD​ ​price,​ ​modeled​ ​as​ ​a​ ​random​ ​walk​ ​(a​ ​monthly​ ​change​ ​isuniformly​ ​random​ ​on​ ​the​ ​interval​ ​[-5%,​ ​5%]).​ ​For​ ​each​ ​miner,​ ​we​ ​also​ ​sample​ ​the​ ​XMR​ ​mined(directly​ ​as​ ​its​ ​estimated​ ​USD​ ​value)​ ​uniformly​ ​randomly​ ​from​ ​the​ ​interval​ ​[$1,​ ​$4].​ ​This​ ​mined
USD​ ​is​ ​added​ ​to​ ​the​ ​bail​ ​fund.
There​ ​needs​ ​to​ ​be​ ​some​ ​decision​ ​mechanism​ ​for​ ​determining​ ​who​ ​the​ ​bail​ ​fund​ ​is​ ​applied
towards.​ ​The​ ​model​ ​optimizes​ ​for​ ​releasing​ ​the​ ​most​ ​people,​ ​so​ ​it​ ​releases​ ​as​ ​many​ ​people​ ​aspossible,​ ​starting​ ​from​ ​the​ ​smallest​ ​bail​ ​amounts.​ ​The​ ​real-world​ ​decision​ ​process​ ​is​ ​obviouslynot​ ​this​ ​neat​ ​and​ ​is​ ​much​ ​more​ ​nuanced.
When​ ​a​ ​person's​ ​pre-trial​ ​detention​ ​time​ ​is​ ​up​ ​and​ ​they​ ​are​ ​out​ ​on​ ​bail​ ​we​ ​see​ ​if​ ​they​ ​appear​ ​fortrial,​ ​according​ ​to​ ​the​ ​FTA​ ​rate​ ​(see​ ​above).​ ​If​ ​they​ ​appear,​ ​we​ ​recoup​ ​the​ ​bail​ ​amount​ ​back​ ​intothe​ ​fund.
This​ ​process​ ​repeats​ ​for​ ​the​ ​number​ ​of​ ​months​ ​specified​ ​by​ ​the​ ​user.
We​ ​run​ ​the​ ​simulation​ ​50​ ​times​ ​and​ ​return​ ​the​ ​means​ ​of​ ​people​ ​released​ ​and​ ​amount​ ​raised
across​ ​all​ ​runs.

References
1. Phillips,​ ​M.​ ​T.​ ​(2012).​ ​A​ ​decade​ ​of​ ​bail​ ​research​ ​in​ ​New​ ​York​ ​City.​ ​CJA,​ ​New​ ​York​ ​City
Criminal​ ​Justice​ ​Agency,​ ​Incorporated.
2. The​ ​Price​ ​of​ ​Freedom:​ ​Bail​ ​and​ ​Pretrial​ ​Detention​ ​of​ ​Low​ ​Income​ ​Nonfelony​ ​Defendantsin​ ​New​ ​York​ ​City​.​ ​December​ ​2,​ ​2010.​ ​Humans​ ​Right​ ​Watch.