SPSV Script v0.2

var ADDON_TITLE = 'SPSV Calculator';
var NUM_KP_BALLOTS = 5;

function onOpen(e) {
  FormApp.getUi()
      .createAddonMenu()
      .addItem('Run Election', 'runElection')
      .addToUi();
}

function onInstall(e) {
  onOpen(e);
}

function runElection() {
  var form = FormApp.getActiveForm();
  var responses = form.getResponses();
  if(responses.length == 0)
    return;

  formItems = form.getItems();

  num_candidates = 0;
  candidate_names = [];
  for(z = 0; z < formItems.length; z++)
    if(formItems[z].getType() == FormApp.ItemType.SCALE)
    {
      num_candidates++;
      candidate_names.push(formItems[z].getTitle());
    }

  rounds = []
  for (var i = 0; i < num_candidates; i++)
    rounds[i] = "Round " + (i + 1);

  var spreadsheet = SpreadsheetApp.create(form.getTitle() + " Results");
  url = spreadsheet.getUrl();
  SpreadsheetApp.openByUrl(url);

  result_sheet = spreadsheet.getActiveSheet();
  result_sheet.setName("Results");

  result_range = result_sheet.getDataRange();
  result_values = result_range.getValues();

  num_ballots = responses.length;

  // create empty score lists
  candidate_scores = [];
  for(c = 0; c < num_candidates; c++)
  {
    candidate_scores[c] = [];
    for(r = 0; r < num_candidates; r++)
      candidate_scores[c][r] = 0;
  }

  // perform the KP transform
  approval_ballots = [];
  for(a = 0; a < num_ballots; a++)
  {
    var response = responses[a];
    var score_ballot = [];

    for(z = 0; z < formItems.length; z++)
      if(formItems[z].getType() == FormApp.ItemType.SCALE)
      {
        var scoreResponse = response.getResponseForItem(formItems[z]);
        if (scoreResponse != null)
          score_ballot.push(parseInt(scoreResponse.getResponse()));
        else
          score_ballot.push(0);
      }

    for(b = 0; b < NUM_KP_BALLOTS; b++)
    {
      var approval_ballot = [];
      for(c = 0; c < num_candidates; c++)
        approval_ballot[c] = score_ballot[c] > b;

      approval_ballots[a * NUM_KP_BALLOTS + b] = approval_ballot;
    }
  }

  // create initial ballot weight list
  weights = [];
  for(k = 0; k < approval_ballots.length; k++)
    weights[k] = 1.0;

  // calculate scores and winners for each round
  elected_candidates = [];
  for(r = 0; r < num_candidates; r++)
  {
    // calculate scores
    for(c = 0; c < num_candidates; c++)
    {
      if(elected_candidates.includes(c))
        candidate_scores[c][r] = -1;
      else
        for(k = 0; k < approval_ballots.length; k++)
          if(approval_ballots[k][c])
            candidate_scores[c][r] += weights[k];
    }

    // calculate winner
    max_score = -1;
    options = [];
    for(c = 0; c < num_candidates; c++)
    {
      if(candidate_scores[c][r] > max_score)
      {
        max_score = candidate_scores[c][r];
        options = [c];
      }
      else if(candidate_scores[c][r] == max_score)
        options.push(c);
    }

    if(options.length > 1)
    {
      // break tie by highest unweighted score
      max_unweighted_score = -1;
      new_options = [];
      for(o = 0; o < options.length; o++)
      {
        option = options[o]
        if(candidate_scores[option][0] > max_unweighted_score)
        {
          max_unweighted_score = candidate_scores[option][0];
          new_options = [option];
        }
        else if(candidate_scores[option][0] == max_unweighted_score)
          new_options.push(option);
      }

      // break any remaining ties pseudorandomly
      elected_candidates[r] = new_options[Math.floor(Math.random() * new_options.length)];
    }
    else
      elected_candidates[r] = options[0];

    // calculate new weights
    for(k = 0; k < approval_ballots.length; k++)
    {
      elected_candidates_approved = 0;
      for(c = 0; c < num_candidates; c++)
        if(approval_ballots[k][c] && elected_candidates.includes(c))
          elected_candidates_approved++;

      weights[k] = 1.0 / (1 + elected_candidates_approved);
    }
  }

  // write results to sheet
  result_sheet.appendRow(['Election Results:']);
  result_sheet.appendRow(['Candidate'].concat(rounds));

  for(c = 0; c < num_candidates; c++)
  {
    result_sheet.appendRow([candidate_names[c]].concat(candidate_scores[c]));
    result_sheet.getRange(3 + c, 2 + elected_candidates.indexOf(c)).setBackgroundRGB(128, 255, 128);
  }

  result_sheet.getRange(3, 2, num_candidates, num_candidates).setNumberFormat("0.##");

  result_sheet.appendRow([' ']);
  result_sheet.appendRow(['Winners'].concat(elected_candidates));
}