Banzhaf Index Calculator

Author: Neo Huang Review By: Nancy Deng
LAST UPDATED: 2024-10-03 16:56:52 TOTAL USAGE: 1993 TAG: Politics Power Index Voting
Unit Converter ▲

Unit Converter ▼

From:	To:
Total Number of Votes:
Vote Weights (comma-separated):
Quota:
Banzhaf Power Index:
      </div>
    </div>
  </div></form>
</div>

<script>
Vue.createApp({
  data() {
    return {
      totalVotes: 0,
      voteWeights: '',
      quota: 0,
      banzhafIndex: ''
    };
  },
  methods: {
    calculateBanzhafIndex() {
      const weights = this.voteWeights.split(',').map(Number);
      const powerIndices = new Array(weights.length).fill(0);
      const totalCombinations = Math.pow(2, weights.length);
      
      for (let i = 1; i < totalCombinations; i++) {
        let sum = 0;
        for (let j = 0; j < weights.length; j++) {
          if (i & (1 << j)) sum += weights[j];
        }
        
        if (sum >= this.quota) {
          for (let j = 0; j < weights.length; j++) {
            if (i & (1 << j)) {
              const withoutPlayerJ = i & ~(1 << j);
              let sumWithoutJ = 0;
              for (let k = 0; k < weights.length; k++) {
                if (withoutPlayerJ & (1 << k)) sumWithoutJ += weights[k];
              }
              
              if (sumWithoutJ < this.quota) {
                powerIndices[j]++;
              }
            }
          }
        }
      }

      const totalPower = powerIndices.reduce((acc, val) => acc + val, 0);
      this.banzhafIndex = powerIndices.map(pi => (pi / totalPower).toFixed(4)).join(', ');
    },
    resetForm() {
      this.totalVotes = 0;
      this.voteWeights = '';
      this.quota = 0;
      this.banzhafIndex = '';
    }
  }
}).mount('#banzhafIndexCalculator');
</script>
    <div class="text-center mt-5  text-slate-500">
        Powered by @Calculator Ultra    </div>
    <div class="flex items-center justify-center mt-2">
        <div class="">
                </div>
    </div>

<div class="rounded-md py-5 hidden">
<a href="https://apps.apple.com/us/app/resolve-calculator/id6670785680">
 <div class="rounded-xl relative w-full h-full flex items-center justify-center">
        <img src="/app.png" alt="resolve-calculator" class="rounded-3xl w-full h-full object-cover">
        <span class="absolute text-white lg:text-4xl text-2xl">Download App</span>
    </div>
</a>
</div>
    </div>

<div class="sm:w-3/5 ml-5 border-t p-3" id="markdown-body">
<div class="text-center font-bold text-2xl text-blue-700">
<h2>Find More Calculator<b >☟</b></h2>
</div>
<div class="relative max-w-3xl mx-auto">
<script async src="https://cse.google.com/cse.js?cx=21850ee7aabcae78b"></script>
<div class="gcse-search"></div>
</div>

<style>
.gs-title{
    text-align: left;
}
.gs-title *{
    font-size: 20px !important;
}
.gsc-search-button-v2{
    padding: 12px 40px;
}
.gsc-input{
    height:30px !important;
    background:none !important;
}
</style>


        <div class="markdown-body">
            <p>The <strong>Banzhaf Power Index</strong> is a measure of the power of individual members in a voting game. It calculates how often a voter can change the outcome of a vote by switching from supporting to opposing a proposal, and vice versa. This calculator allows you to input the total number of votes, the vote weights of each player, and the quota needed to pass a motion. The result is the Banzhaf Power Index for each player, indicating their relative power in the decision-making process.</p>
<h3>Historical Background</h3>
<p>The Banzhaf Power Index was introduced by John F. Banzhaf III in 1965 as a method to measure voting power in decision-making bodies. It is particularly relevant in political science and economics, where it helps to quantify the influence of individual voters or groups within a larger voting system.</p>
<h3>Calculation Formula</h3>
<p>The formula to calculate the Banzhaf Power Index involves considering all possible voting combinations and determining the number of times a voter is critical in reaching the quota. The power index is then the proportion of times each voter is critical, relative to the total number of critical occurrences.</p>
<h3>Example Calculation</h3>
<p>Consider a voting system with three players where the vote weights are 4, 3, and 2, and the quota is 6. The Banzhaf Power Index would be calculated by evaluating all possible coalitions and determining when each player is pivotal in meeting or exceeding the quota.</p>
<h3>Importance and Usage Scenarios</h3>
<p>The Banzhaf Power Index is crucial for understanding the dynamics of collective decision-making processes, particularly in political bodies, corporate boards, or any scenario where decisions are made by voting. It helps to highlight the disproportionate power that some voters may hold due to their ability to influence outcomes.</p>
<h3>Common FAQs</h3>
<ol>
<li>
<p><strong>What is the Banzhaf Power Index used for?</strong></p>
<ul>
<li>The Banzhaf Power Index is used to measure the power or influence of individual members in a voting system. It is often applied in political science to assess the power distribution within legislative bodies.</li>
</ul>
</li>
<li>
<p><strong>How does the Banzhaf Power Index differ from other power indices?</strong></p>
<ul>
<li>The Banzhaf Power Index focuses on a voter's ability to change the outcome of a vote by changing their vote, while other indices like the Shapley-Shubik Index consider different aspects of power distribution.</li>
</ul>
</li>
<li>
<p><strong>Can the Banzhaf Power Index be applied to any voting system?</strong></p>
<ul>
<li>Yes, it can be applied to any voting system where decisions are made based on the aggregation of votes with different weights. However, its effectiveness depends on the complexity of the voting system.</li>
</ul>
</li>
</ol>
<p>This calculator helps users understand the influence each voter has in a decision-making process, making it a valuable tool for analyzing power distribution in voting systems.</p>        </div>



    </div>
</div>

<h2 class="m-2 font-bold">Recommend</h2>

<div class="
grid
grid-cols-1
sm:grid-cols-2
md:grid-cols-3
lg:grid-cols-4
gap-4
">
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/gcs-calculator.html">
            <span>GCS Calculator</span>
        </a>
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/crushed-shell-calculator.html">
            <span>Crushed Shell Calculator</span>
        </a>
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/gtts-per-minute-calculator.html">
            <span>GTTS Per Minute Calculator</span>
        </a>
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/binding-quilt-calculator.html">
            <span>Binding Quilt Calculator</span>
        </a>
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/grassland-fire-danger-index-calculator.html">
            <span>Grassland Fire Danger Index Calculator</span>
        </a>
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/pa-to-cfm-calculator.html">
            <span>Pa To Cfm Calculator</span>
        </a>
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/picks-theorem-calculator.html">
            <span>Pick’s Theorem Calculator</span>
        </a>
            <a class="
        shadow-xl shadow-black/5
        ring-1 ring-slate-700/10
        hover:bg-slate-50
        rounded-md border-blue-500 text-blue-800 p-10 text-center font-bold" href="https://www.calculatorultra.com/en/tool/span-efficiency-factor-calculator.html">
            <span>Span Efficiency Factor Calculator</span>
        </a>
    </div>

</div>
    </div>
    <footer class="mx-auto mt-32 w-full max-w-container px-4 sm:px-6 lg:px-8">
    <div class="border-t border-slate-900/5 py-10">


    <p class="mt-5 text-center text-sm leading-6 text-slate-500">© 2024 <a href="https://www.calculatorultra.com">Calculator Ultra</a> . All rights reserved.</p>

        <div class="mt-5 flex items-center justify-center space-x-4 text-sm font-semibold leading-6 text-slate-700">

            <a href="/en/terms-of-use">Terms of Use</a>

            <div class="h-4 w-px bg-slate-500/20"></div>

            <a href="/en/about">About</a>

            <div class="h-4 w-px bg-slate-500/20"></div>

<div id="lang-select" class="flex">
<span class="block w-full py-2 bg-white rounded-md ">
Language:
</span>
    <select id="languageSelect" class="block w-full px-4 py-2 bg-white border rounded-md shadow-sm focus:border-blue-500 focus:ring focus:ring-blue-200 focus:ring-opacity-50"
            @change="changeLanguage($event)" :value="defaultLanguage">
        <option value="en">🇬🇧 English</option>
        <option value="zh">🇨🇳 中文</option>
        <option value="es">🇪🇸 Español</option>
        <option value="fr">🇫🇷 Français</option>
        <option value="ar">🇸🇦 العربية</option>
        <option value="pt">🇵🇹 Português</option>
        <option value="hi">🇮🇳 हिन्दी</option>
        <option value="ru">🇷🇺 Русский</option>
        <option value="ja">🇯🇵 日本語</option>
        <option value="ko">🇰🇷 한국어</option>
        <option value="bn">🇧🇩 বাংলা</option>
        <option value="pa">🇮🇳 ਪੰਜਾਬੀ</option>
        <option value="de">🇩🇪 Deutsch</option>
        <option value="jv">🇮🇩 Basa Jawa</option>
        <option value="mr">🇮🇳 मराठी</option>
        <option value="tr">🇹🇷 Türkçe</option>
        <option value="ta">🇮🇳 தமிழ்</option>
        <option value="vi">🇻🇳 Tiếng Việt</option>
        <option value="th">🇹🇭 ไทย</option>
    </select>
</div>
<script>

Vue.createApp({
    data() {
    return {
        defaultLanguage: this.getDefaultLanguage(),
    };
},
methods: {
    getDefaultLanguage() {
        const path = window.location.pathname;
        const langMatch = path.match(/\/(en|zh|es|fr|ar|pt|hi|ru|ja|ko|bn|pa|de|jv|mr|tr|ta|vi|th)\//);
        return langMatch ? langMatch[1] : 'en'; // 默认为 'en'，如果 URL 中没有匹配到语言代码
    },
    changeLanguage(event) {
        const selectedLanguage = event.target.value;
        let newPath = window.location.pathname.replace(/\/(en|zh|es|fr|ar|pt|hi|ru|ja|ko|bn|pa|de|jv|mr|tr|ta|vi|th)\//, `/${selectedLanguage}/`);
        if(!window.location.pathname.match(/\/(en|zh|es|fr|ar|pt|hi|ru|ja|ko|bn|pa|de|jv|mr|tr|ta|vi|th)\//)){
            newPath = "/"+selectedLanguage+"/";
        }
        window.location = newPath + window.location.search;
    }
},
}).mount('#lang-select');

// 捕获全局的 JavaScript 错误
window.onerror = function (message, source, lineno, colno, error) {
    // 构建错误信息对象
    const errorDetails = {
        message: message, // 错误消息
        source: source, // 发生错误的脚本文件
        lineno: lineno, // 出现错误的行号
        colno: colno, // 出现错误的列号
        stack: error ? error.stack : '' // 错误的堆栈信息（如果可用）
    };

    // 使用 fetch 将错误信息发送到指定的 API 端点
    fetch('/Api/LogJsError', {
        method: 'POST',
        headers: {
            'Content-Type': 'application/json'
        },
        body: JSON.stringify(errorDetails)
    });

    // 阻止默认的错误处理行为
    return true;
};

// 捕获资源加载错误（例如图片、脚本、样式等）
window.addEventListener('error', function (event) {
    // 资源错误一般是由 `event.target` 触发的
    if (event.target && (event.target instanceof HTMLScriptElement ||
        event.target instanceof HTMLLinkElement ||
        event.target instanceof HTMLImageElement)) {
        const errorDetails = {
            message: `Resource Load Error: ${event.target.src || event.target.href}`,
            source: event.target.nodeName,
            lineno: 0,
            colno: 0,
            stack: ''
        };
        if(event.target.nodeName.indexOf("KaTeX") != -1
            || event.target.nodeName.indexOf("google") != -1
        ){
            return
        }

        fetch('/Api/LogJsError', {
            method: 'POST',
            headers: {
                'Content-Type': 'application/json'
            },
            body: JSON.stringify(errorDetails)
        });
    }
}, true);

</script>

        </div>
    </div>
</footer>
</body>
<style>
</style>
</html>