44:["$","title",null,{"children":"Wait For Quiet Algorithm | Chad Nauseam | Observable"}] 4c:T438,Plot.plot({ style: "overflow: visible;", marks: [ Plot.line(sub_end_time(wait_for_delay_end_times), { x: "timestep", y: "time_remaining", z: -1, stroke: time_remaining_color }), Plot.line( sub_end_time([ { timestep: 0, end_time: initial_voting_period }, { timestep: initial_voting_period, end_time: initial_voting_period } ]), { x: "timestep", y: "time_remaining" } ), Plot.line( [ { timestep: 0, time_remaining: (1 / 2) * initial_voting_period + wait_for_quiet_deadline_increase_seconds }, { timestep: initial_voting_period + wait_for_quiet_deadline_increase_seconds * 2, time_remaining: 0 } ], { x: "timestep", y: "time_remaining", stroke: `${wait_for_quiet_line_color}`, strokeOpacity: 0.2 } ), Plot.ruleX( flips.map((x) => ({ x })), { x: "x", strokeOpacity: 0.1 } ) ] })4d:T701,wait_for_delay_end_times = { let pairs = _.tail( [0, ...flips].map((fliptime, index, arr) => ({ previous: arr[index - 1], current: fliptime })) ); const initial_time_series = [ { timestep: 0, end_time: initial_voting_period } ]; let previous_end_time = initial_voting_period; let extended_time_series = _.concat( initial_time_series, pairs.flatMap((flip_info) => { let previous_flip_time_info = flip_info.previous !== 0 ? { timestep: flip_info.current, end_time: end_time( wait_for_quiet_deadline_increase_seconds, initial_voting_period, flip_info.previous ), previous: true } : { timestep: flip_info.current, end_time: initial_voting_period, previous: true }; let current_flip_time_info = { timestep: flip_info.current, end_time: end_time( wait_for_quiet_deadline_increase_seconds, initial_voting_period, flip_info.current ) }; console.log(current_flip_time_info, previous_end_time); if ( current_flip_time_info.timestep <= previous_flip_time_info.end_time && current_flip_time_info.timestep <= previous_end_time ) { previous_end_time = current_flip_time_info.end_time; return [previous_flip_time_info, current_flip_time_info]; } else { return []; } }, []) ); console.log("========"); const endtime = extended_time_series[extended_time_series.length - 1].end_time; extended_time_series.push({ timestep: endtime, end_time: endtime }); return extended_time_series; }4e:[] 48:{"id":"0bfdfc6a0d111944","slug":"wait-for-quiet-algorithm","title":"Wait For Quiet Algorithm","thumbnail":"009e12571f1416c5ed1973bbf0096b350e436b09cf716c53432a1888c0d118a6","access_level":"public","create_time":"$D2022-07-04T18:00:30.385Z","update_time":"$D2022-07-15T21:35:20.354Z","view_time":null,"first_public_time":"$D2022-07-14T00:00:49.301Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"bcbc8b7a391cae0f","login":"anchpop","name":"Chad Nauseam","avatar_url":"https://avatars-next.observableusercontent.com/631db6913bbef8cd58406196aad9cc7c6a74a4c04e20bf62197f02aa24e1aada","tier":"starter_2024","bio":"wanna get a mansion, a jacuzzi, a theater to watch my movies\n","followed_by_you":false,"follows_you":false},"version":497,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"061d7bea4b9535b9","login":"anchpop","name":"Chad Nauseam","avatar_url":"https://avatars-next.observableusercontent.com/631db6913bbef8cd58406196aad9cc7c6a74a4c04e20bf62197f02aa24e1aada","tier":null,"bio":"wanna get a mansion, a jacuzzi, a theater to watch my movies\n","followed_by_you":false,"follows_you":false}],"members":[{"type":"individual","id":"061d7bea4b9535b9","login":"anchpop","name":"Chad Nauseam","avatar_url":"https://avatars-next.observableusercontent.com/631db6913bbef8cd58406196aad9cc7c6a74a4c04e20bf62197f02aa24e1aada","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Wait For Quiet Algorithm","cells":[{"id":0,"value":"# Wait For Quiet Algorithm","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":344,"value":"## Purpose","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":346,"value":"The purpose of the wait for quiet algorithm is to extend the voting period on a proposal if it *flips* when the vote is close to ending.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":349,"value":"This makes sure everyone gets a chance to vote, even if the outcome changes right before voting was going to expire.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":86,"value":"## Example","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":105,"value":"viewof initial_voting_period = Inputs.range([0, 100], {\n label: \"initial voting period\",\n step: 1,\n value: 30\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":111,"value":"viewof wait_for_quiet_deadline_increase_seconds = Inputs.range([0, 100], {\n label: \"wait for quiet deadline increase\",\n step: 1,\n value: 10\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":114,"value":"viewof flips_raw = Inputs.text({ label: \"Flips\", value: \"25, 33, 40, 44, 46\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":410,"value":"Flips are at timesteps ${flips.join(`, `)}.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":406,"value":"See the adjusted time remaining in red, and the original in **black**:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":119,"value":"$4c","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":384,"value":"#### Legend:\n\n**black**: time remaining in the initial voting period \nred: the adjusted time remaining \nblue: a conceptual line to show how the red line behaves","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":471,"value":"## Intuitive Explanation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":474,"value":"The **black** line shows the time remaining in the original voting period, so it goes down at a ${tex`45^{\\circ}`} angle. \n\nThe blue line goes down at half the rate of the **black** line, which happens to be a ${tex`45/2 = 22.5^{\\circ}`} angle.\n\nThe red line shows the time remaining as adjusted by the wait-for-quiet algorithm. Whenever there's a flip in the vote total, the time remaining is \"bumped up\" to the blue line, if the blue line is above than the **black** line at that time.\n\nYou can think of the blue line as showing \"what would the wait-for-quiet algorithm adjust the time-remaining to if there were a flip at this time.\"","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":342,"value":"## Mathematical Explanation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":88,"value":"Copied from [governance/src/proposal.rs](https://gitlab.com/dfinity-lab/public/ic/blob/master/rs/sns/governance/src/proposal.rs#L580-611)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":41,"value":"Let ${tex`W`} be short for `wait_for_quiet_deadline_increase_seconds`. A proposal's voting\nperiod starts with an `initial_voting_period` and can be extended\nto at most ${tex`\\text{initial voting period} + 2 * W`}.\nThe `required_margin` reflects the proposed deadline extension to be\nmade beyond the current moment, so long as that extends beyond the\ncurrent wait-for-quiet deadline. We calculate the `required_margin` a\nbit indirectly here so as to keep with unsigned integers, but the\nidea is:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":365,"value":"viewof elapsed = Inputs.range([0, 100], {\n label: \"elapsed\",\n step: 1,\n value: 30\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":49,"value":"\\text{required margin} \n\\, {\\color{blue} (=${(required_margin(wait_for_quiet_deadline_increase_seconds, initial_voting_period, elapsed)).toFixed(1)}}) \n= \nW \\, {\\color{blue} (=${wait_for_quiet_deadline_increase_seconds})} \n + {\n \\text{initial voting period} \\, {\\color{blue} (=${initial_voting_period}}) - \n \\text{elapsed} \\, {\\color{blue} (=${elapsed})} \n \\over{2}}","pinned":false,"hidden":false,"mode":"tex","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":70,"value":"Thus, while we are still within the initial voting period, we add\nto W, but once we are beyond that window, we subtract from W until\nreaching the limit where `required_margin` remains at zero. This\noccurs when:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":73,"value":"\\text{elapsed} = \\text{initial voting period} + 2 * W","pinned":false,"hidden":false,"mode":"tex","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":77,"value":"As an example, given that ${tex`W = ${wait_for_quiet_deadline_increase_seconds}h`}, if the `initial_voting_period` is\n`${initial_voting_period}h` then the maximum deadline will be ${tex`{\\color{blue} ${initial_voting_period}}\\text{h} + 2 * {\\color{blue} ${wait_for_quiet_deadline_increase_seconds}}\\text{h} = ${initial_voting_period + 2 * wait_for_quiet_deadline_increase_seconds}\\text{h}`}.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":82,"value":"The required_margin ends up being a linearly decreasing value,\nstarting at ${tex`W + {\\text{initial voting period} \\over{2}}`} and reducing to zero at the\nfurthest possible deadline. When the vote does not flip, we do not\nupdate the deadline, and so there is a chance of ending prior to\nthe extreme limit. But each time the vote flips, we \"re-enter\" the\nlinear progression according to the elapsed time.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":84,"value":"This means that whenever there is a flip, the deadline is always\nset to the current time plus the required_margin, which places us\nalong the linear path that was determined by the starting\nvariables.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":97,"value":"## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":386,"value":"sub_end_time = (data) =>\n data.map((o) => ({\n timestep: o.timestep,\n time_remaining: o.end_time - o.timestep\n }))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"required_margin = (w, initial_voting_period, elapsed) =>\n w + ((initial_voting_period - elapsed) / 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"end_time = (w, initial_voting_period, elapsed) =>\n Math.max(\n elapsed + required_margin(w, initial_voting_period, elapsed),\n initial_voting_period\n )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"flips = flips_raw\n .split(\", \")\n .filter((x) => x !== \"\")\n .map((x) => parseInt(x))\n .filter((x) => x !== 0)\n .sort((a, b) => a - b)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":133,"value":"$4d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":253,"value":"endtime =\n wait_for_delay_end_times[wait_for_delay_end_times.length - 1].end_time;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":162,"value":"_ = {\n const [_, fp] = await Promise.all([\n require(\"lodash@4\"),\n require(\"https://cdn.jsdelivr.net/gh/lodash/lodash@4/dist/lodash.fp.min.js\")\n ]);\n return fp(_);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":395,"value":"time_remaining_color = \"#F24333\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":453,"value":"wait_for_quiet_line_color = \"#0000FF\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4e","stdlib":"1"}} 24:null