{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"# The Trigger Function\n",
"\n",
"## Transforming Continuous Preferences into Discrete Events\n",
"\n",
"This notebook is a mathematical deep dive into the derivation of the Trigger Function used in Conviction Voting for the 1Hive use case.\n",
"\n",
"The role of the trigger function in the conviction voting algorithm is to determine if a sufficient amount of conviction has accumulated in support of a particular proposal, at which point it passes from being a candidate proposal to an active proposal. \n",
"\n",
"In the 1Hive use case for conviction, proposals map to precise quantities of resources $r$ requested from a communal resource pool $R$ (which is time varying $R_t$ but we will drop the subscript for ease of reading). Furthermore, there is a supply of governance tokens $S$ which are being used as part of the goverance process. In the implementation the quantity $S$ will be the effective supply which is the subset of the total Supply for the governance token in question. \n",
"\n",
"We assume a time varying supply $S_t$ and therefore we can interpret $S_t$ as the effective supply without loss of generality. From here forward, we will drop the subscript and refer to $S$ for ease of reading. The process of passing a proposal results in an allocation of $r$ funds as shown in the figure below.\n",
"\n",
"![](images/stockflow_cv_trigger.png)\n",
"\n",
"This diagram shows the trigger function logic, which depends on token supply $S$, total resources available $R$ and total conviction $y$ at time $t$, as well as the proposal's requested resources $r$, the maximum share of funds a proposal can take ($\\beta$) and a tuning parameter for the trigger function ($\\rho$). Essentially, this function controls the maximum amount of funds that can be requested by a proposal ($\\beta$), using an equation resembling electron repulsion to ensure conviction increases massively beyond that point, so that no proposals may request more than $\\beta$ share of total funds.\n",
"\n",
" \n",
"\n",
"## Parameter Definition\n",
"\n",
"* $\\alpha \\in (0,1)$ is the parameter that determines the half life decay rate of conviction, as defined in the [Deriving Alpha notebook](https://nbviewer.jupyter.org/github/BlockScience/Aragon_Conviction_Voting/blob/master/models/v3/Deriving_Alpha.ipynb) and should be tuned according to a desired half life.\n",
"\n",
"* $\\beta\\in (0,1)$ is the max % of total funds that can be discharged by a single proposal, and is the asymptotic limit for the trigger function. It is impossible to discharge more than $\\beta$ share of funds. \n",
"\n",
"* $\\rho \\in (0, \\beta^2)$ is a the scale factor for the trigger function. Note that we require $0<\\rho <\\beta^2$ \n",
"\n",
"The trigger function is defined by: $y^*(r) = \\frac{\\rho S}{(1-\\alpha)\\left(\\beta - \\frac{r}{R}\\right)^2 }$\n",
"\n",
"The geometric properties of this function with respect to the parameter choices are shown here:\n",
"\n",
"![](images/trigger_geometry.png)\n",
"\n",
"On this plot we can see that there is a maximum conviction that can be reached for a proposal, and also a maximum achievable funds released for a single proposal, which are important bounds for a community to establish for their funding pool. \n",
"\n",
"Note that by requiring that: $0<\\rho <\\beta^2$ the following holds $0<\\frac{\\rho}{\\beta^2}<1$ and $0<\\beta - \\sqrt \\rho <\\beta <1$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initializing Conditions for Plot Series"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import inspect\n",
"\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n",
"from cadCAD.configuration.utils import config_sim\n",
"from model.parts.utils import *\n",
"from model.parts.sys_params import * "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'sentiment': 0.6, 'n': 30, 'm': 7, 'funds': 4867.21, 'supply': 22392.22}"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"initial_values"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'beta': [0.2],\n",
" 'rho': [0.0025],\n",
" 'alpha': [0.7937005259840998],\n",
" 'gamma': [0.001],\n",
" 'sensitivity': [0.75],\n",
" 'tmin': [1],\n",
" 'min_supp': [1],\n",
" 'base_completion_rate': [45],\n",
" 'base_failure_rate': [180],\n",
" 'base_engagement_rate': [0.3],\n",
" 'lowest_affinity_to_support': [0.3]}"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"params"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"supply = initial_values['supply']\n",
"funds = initial_values['funds']\n",
"\n",
"alpha = params['alpha'][0]\n",
"beta = params['beta'][0]\n",
"rho = params['rho'][0]\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def trigger(requested, funds, supply, alpha, beta, rho):\n",
" '''\n",
" Function that determines threshold for proposals being accepted.\n",
" Refactored slightly from built in to be explicit for demo\n",
" '''\n",
" share = requested/funds\n",
" if share < beta:\n",
" threshold = rho*supply/(beta-share)**2 * 1/(1-alpha)\n",
" return threshold \n",
" else: \n",
" return np.inf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The actual trigger function used in the V3 simulation is below:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def trigger_threshold(requested, funds, supply, alpha, params):\n",
" '''\n",
" Description:\n",
" Function that determines threshold for proposals being accepted. \n",
"\n",
" Parameters:\n",
" requested: float, funds requested\n",
" funds: float, funds\n",
" supply: float\n",
" alpha: float\n",
" params: dictionary of parameters as floats\n",
"\n",
" Returns:\n",
" Threshold value\n",
" '''\n",
"\n",
" share = requested/funds\n",
" if share < params['beta']:\n",
" threshold = params['rho']*supply/(params['beta']-share)**2 * 1/(1-alpha)\n",
" return threshold \n",
" else: \n",
" return np.inf\n",
"\n"
]
}
],
"source": [
"trigger_simulation = inspect.getsource(trigger_threshold)\n",
"print(trigger_simulation)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simple derivations\n",
"We can plug in some boundary conditions to determine our minimum required and maximum achievable conviction. We can also determine the maximum achievable funds a proposal is able to request, to understand the upper bounds of individual proposal funding.\n",
"\n",
"* min_required_conviction = $y^*(0) = \\frac{\\rho S}{(1-\\alpha)\\beta^2}$\n",
"* max_achievable_conviction = $\\frac{S}{1-\\alpha}$\n",
"* min_required_conviction_as_a_share_of_max = $\\frac{\\rho S}{(1-\\alpha)\\beta^2} \\cdot \\frac{1-\\alpha}{S} = \\frac{\\rho}{\\beta^2}$\n",
"* To compute the max_achievable_request solve: $\\frac{S}{1-\\alpha} = \\frac{\\rho S}{(1-\\alpha)\\left(\\beta-\\\\frac{r}{R}\\right)^2}$\n",
"* max_achievable_request = $r = (\\beta -\\sqrt\\rho)F$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"min_required_conviction = 6783.893932236272\n",
"max_achievable_conviction = 108542.30291578037\n",
"\n",
"min_achievable_conviction_as_a_share_of_max_achievable_conviction = 0.06249999999999999\n",
"\n",
"max_achievable_request = 730.0815000000001\n",
"total_funds = 4867.21\n",
"\n",
"max_achievable_request_as_a_share_of_funds = 0.15000000000000002\n"
]
}
],
"source": [
"min_required_conviction = trigger(0, funds, supply, alpha, beta, rho)\n",
"print(\"min_required_conviction = \"+str(min_required_conviction))\n",
"\n",
"max_achievable_conviction = supply/(1-alpha)\n",
"print(\"max_achievable_conviction = \"+str(max_achievable_conviction))\n",
"print(\"\")\n",
"print(\"min_achievable_conviction_as_a_share_of_max_achievable_conviction = \"+str(min_required_conviction/max_achievable_conviction))\n",
"print(\"\")\n",
"max_request = beta*funds\n",
"max_achievable_request = (beta - np.sqrt(rho))*funds\n",
"print(\"max_achievable_request = \"+str(max_achievable_request))\n",
"print(\"total_funds = \"+str(funds))\n",
"print(\"\")\n",
"print(\"max_achievable_request_as_a_share_of_funds = \"+str(max_achievable_request/funds))\n",
"\n",
"granularity = 100 \n",
"\n",
"requests = np.arange(0,.9*max_request, max_request/granularity)\n",
"requests_as_share_of_funds = requests/funds\n",
"conviction_required = np.array([trigger(r, funds, supply, alpha, beta, rho) for r in requests])\n",
"conviction_required_as_share_of_max = conviction_required/max_achievable_conviction\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot series 1: Examining the Shape of the Trigger Function Compared to Absolute Funds Requested \n",
"\n",
"These plots demonstrate the trigger function shape, showing how the amount of conviction required increases as amount of requested (absolute) funds increases. These plots are based on alpha, Supply and Funds as initialized above."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"shape_of_trigger_in_absolute_terms(requests, conviction_required,max_request,\n",
" max_achievable_request,max_achievable_conviction,\n",
" min_required_conviction)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"shape_of_trigger_in_absolute_terms(requests, conviction_required,max_request,\n",
" max_achievable_request,max_achievable_conviction,\n",
" min_required_conviction,log=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above plots look at the shape of the trigger function on a linear and log scale, where you can see conviction required to pass a proposal increase with the absolute amount of funds requested. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot series 2: Examining the Shape of the Trigger Function Compared to Relative Funds Requested \n",
"\n",
"These plots demonstrate the trigger function shape, showing how the amount of conviction required increases as the **proportion** of requested funds (relative to total funds) increases. These plots are based on alpha, Supply and Funds as initialized above."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"shape_of_trigger_in_relative_terms(requests_as_share_of_funds, conviction_required_as_share_of_max\n",
" ,max_request, funds, max_achievable_request,\n",
" max_achievable_conviction,\n",
" min_required_conviction)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"shape_of_trigger_in_relative_terms(requests_as_share_of_funds, conviction_required_as_share_of_max\n",
" ,max_request, funds, max_achievable_request,\n",
" max_achievable_conviction,\n",
" min_required_conviction,log=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above plots look at the shape of the trigger function on a linear and log scale, where you can see conviction required to pass a proposal increase with the percentage of total funds requested. The two green lines intersect at persistent, unanimous support for a proposal, and the maximum that can be requested (in this case) is 15% of the total pool of funds."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot series 3: Heat Maps\n",
"\n",
"The next set of plots show that conviction required increases to a maximum with the proportion of total funds requested, capping out (in this case) at 15% of total funds available. Note that since we are using **relative** funds requested, these plots are invariant to alpha and effective supply. (In other words, since we are only looking at funds requested relative to the total funds, which are both affected by changes in alpha or effective supply, our conviction required for relative funds requested remains unchanged)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"{'beta': [0.2],\n",
" 'rho': [0.0025],\n",
" 'alpha': [0.7937005259840998],\n",
" 'gamma': [0.001],\n",
" 'sensitivity': [0.75],\n",
" 'tmin': [1],\n",
" 'min_supp': [1],\n",
" 'base_completion_rate': [45],\n",
" 'base_failure_rate': [180],\n",
" 'base_engagement_rate': [0.3],\n",
" 'lowest_affinity_to_support': [0.3]}"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"params"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"supply_sweep = trigger_sweep('effective_supply',trigger, params, supply)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"alpha_sweep = trigger_sweep('alpha',trigger, params, supply)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"trigger_grid(supply_sweep, alpha_sweep)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conclusion\n",
"\n",
"We recommend that implementers take careful consideration of their choices of the $\\beta$ (% of total funds that can be requested) and $\\rho$ (scaling factor) parameters, as these will have a high impact on your system design. $\\alpha$ and other parameters are calculable from these parameters, but matter less when considering proposals requesting relative share of total funds.\n",
"\n",
"To get a feel for how $\\beta$ and $\\rho$ impact the trigger function, play around with this [desmos graph](https://www.desmos.com/calculator/yxklrjs5m3). (Note: this is just a tool to play with the curve shape, don't be confused by variable names! $\\rho$ is w in the calculator, due to the lack of greek characters ;)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}