<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">AJCM</journal-id><journal-title-group><journal-title>American Journal of Computational Mathematics</journal-title></journal-title-group><issn pub-type="epub">2161-1203</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/ajcm.2022.124027</article-id><article-id pub-id-type="publisher-id">AJCM-122148</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Physics&amp;Mathematics</subject></subj-group></article-categories><title-group><article-title>
 
 
  A Mathematical Model of Global Equity for Allocating Asteroid Resources Based on Analytic Hierarchy Process
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Shuyang</surname><given-names>Qian</given-names></name><xref ref-type="aff" rid="aff1"><sub>1</sub></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>Department of Management, Shanghai University, Shanghai, China</addr-line></aff><pub-date pub-type="epub"><day>18</day><month>10</month><year>2022</year></pub-date><volume>12</volume><issue>04</issue><fpage>372</fpage><lpage>380</lpage><history><date date-type="received"><day>11,</day>	<month>May</month>	<year>2022</year></date><date date-type="rev-recd"><day>27,</day>	<month>December</month>	<year>2022</year>	</date><date date-type="accepted"><day>30,</day>	<month>December</month>	<year>2022</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  As the Earth’s resources are utilized, we are increasingly seeking access to space-based resources. One of the most promising solutions to the problem of resource scarcity is asteroid mining. However, it brings with it the problem of resource allocation. Because of the different levels of development of countries, the way of equal distribution is not reasonable. In this paper, we firstly elaborate and define the abstract global equity in a concrete way, linking global equity with comprehensive national strength, and build a new global equity model on this basis. In this way, we can apply the established model to the distribution of space-based resources or other resources. This paper first establishes the corresponding relation between global equity and comprehensive national power, and then determines several important indexes affecting comprehensive national power according to Klein equation. Further, this paper selected four representative large countries and determined the data of each country in each important index by consulting relevant materials. On this basis, the analytic hierarchy process was used to determine the weight of each country in resource allocation. By comparing the weight index obtained by the model in this paper with the actual resource allocation ratio, we can find that they are in good agreement 
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   Therefore, it can be concluded that when allocating space-based resources or other resources, we can use the global equity model established in this paper to calculate the weight index and allocate resources on this basis to ensure the realization of global equity 
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</p></abstract><kwd-group><kwd>Hierarchical Analysis</kwd><kwd> Global Equity Resource</kwd><kwd> Allocation Mod</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>The United Nations in 1976 the UN outer space treaty, so far, most of the world’s countries have signed the treaty, agreed to the “exploration and use of outer space, including the moon and other celestial bodies, the interests and rights for all countries, regardless of their economic and scientific development, outer space should be the land of mankind” [<xref ref-type="bibr" rid="scirp.122148-ref3">3</xref>]. Research suggests that there are more than 16,000 asteroids with orbits like Earth’s near Earth, many of which contain resources that are increasingly scarce on Earth [<xref ref-type="bibr" rid="scirp.122148-ref4">4</xref>]. Therefore, by exploiting the resources of asteroids, humans can relieve the shortage of resources caused by the rapid development of heavy industry on Earth [<xref ref-type="bibr" rid="scirp.122148-ref5">5</xref>]. However, due to the difficulty of exploiting resources in outer space and the possible waste of resources caused by blind exploitation, [<xref ref-type="bibr" rid="scirp.122148-ref6">6</xref>] it is necessary for us to unify opinions within the Earth, formulate corresponding mining strategies and carry out reasonable and fair distribution on this basis, so as to increase global equity and promote the overall development of the human community [<xref ref-type="bibr" rid="scirp.122148-ref7">7</xref>]. In this paper, the analytic hierarchy process is mainly used to measure global equity. By selecting several important indicators and representative countries, the analytic hierarchy process model is used to obtain the proportion of resources allocated by corresponding countries, which can better meet the overall requirements of global equity.</p></sec><sec id="s2"><title>2. Global Equity Model</title><sec id="s2_1"><title>2.1. Background of Model</title><p>Global equity refers to distributing resources according to the contribution of different countries to the world, not evenly distributed in the general sense. In brief, what you deserve matches what you get. We use comprehensive national power [<xref ref-type="bibr" rid="scirp.122148-ref8">8</xref>] to reflect global equity because countries with greater comprehensive national power contribute more to the global economy, in politics, no matter in economics, science or technology. For example, the US and China account for a high proportion of GDP in each country or region to global GDP, at around 23.92% and 18.45%. But India accounts for 3.22% then India’s contribution to the world is lower relative to the U.S. and China. On the other hand, when a country achieves outstanding results, other countries will follow it and thus promoting global development. We believe that the “fairness” is “what you deserve matches what you get” so the country that contributes more deserves more resources when it comes to resource allocation.</p><p>After the 1970s, a scholar of international issues and strategic studies, R.S. Klein of the United States, conducted a more extensive and in-depth exploration in the quantitative studies of comprehensive national power. In his three works Evaluation of World Power, Evaluation of World Power 1977 and World Power Trends and U.S. Foreign Policy in the 1980s published in 1975, 1977 and 1980 respectively, he proposed a mathematical model for measuring and assessing a country’s national power based on the kernel of the recent geopolitical doctrine of national power: P<sub>N</sub> = (C + E + W) &#215; (S + W). P<sub>N</sub> is the composite national power index; C is the basic entity, consisting of population and land area; E is the economic power, consisting of six categories of indicators, including GDP, energy, critical non-fuel minerals, industrial production capacity, food production, and foreign trade; M is the military power, expressed as the sum of strategic nuclear forces and conventional forces possessed by a country; S is the power of a country conventional forces; S is strategic objectives, which refers to the political goals to be achieved and national interests to be protected in the international environment; W is the will to pursue national strategy, which refers to a country’s ability to mobilize its citizens to support the government’s defense and foreign policy. As the pioneer of national power measurement, Klein equation has great authority and reference value. So, we choose four important factors in Klein equation as our evaluation index, which are population, land area, GDP, and military power. They account for the national power calculation weights of 10%, 10%, 40%, and 40%, respectively (There is no influence factor brought by science and technology in Klein’s equation, then we decided that the science and technology factor has been reflected in the economic power and military power side-by-side because of the wide range of factors involved and influenced by science and technology, and the degree of change of science and technology is so fast due to historical development that it is more complicated and inaccurate to strip the weights separately).</p><p>We visualized the data:</p><p>China and India have large differences in population size from the other countries and are more dominant in terms of population size; as shown in <xref ref-type="fig" rid="fig1">Figure 1</xref>.</p><p>Russia, Canada, China, and the United States account for a large portion of the world’s land area, and these countries are more dominant in terms of regional size to assess national power; as shown in <xref ref-type="fig" rid="fig2">Figure 2</xref>.</p><p>The United States, Japan’s national GDP is bigger, then the economic strength is higher, the national strength of these countries more dominant; as shown in <xref ref-type="fig" rid="fig3">Figure 3</xref>.</p><p>The lower the ratio, the stronger the military power. If the United States, Russia, and China have more military power, then the judging of national power will be more dominant; as shown in <xref ref-type="fig" rid="fig4">Figure 4</xref>.</p></sec><sec id="s2_2"><title>2.2. Build the Hierarchical Model</title><p>Analytic hierarchy process (AHP) is a decision analysis method which combines qualitative and quantitative methods to solve multi-objective complex problems. The method uses the decision maker’s experience to determine the relative importance between the criteria for the achievability of each measure of the objectives. The proportion of the country power calculation weights has been determined, and a comparative value for these four trade-off indicators that allows for fair feedback in each country needs to be determined.</p><p>The decision problem is now decomposed into three levels, the top level is the objective level M, which is to develop a reasonable global equity evaluation system, the middle level is the criterion level, including population C1, land area C2, GDP C3, and military power C4, and the bottom level is the program level, which is the individual countries with global autonomy, indicated by P1, P2…Pn. To simplify the hierarchical model and control the ratio b greater than 0 and less than 10, we choose the United States, China, India, and Pakistan as representative countries for the calculation of their comprehensive national power [<xref ref-type="bibr" rid="scirp.122148-ref9">9</xref>]; as shown in <xref ref-type="fig" rid="fig5">Figure 5</xref> below.</p></sec><sec id="s2_3"><title>2.3. Model Solution</title><sec id="s2_3_1"><title>2.3.1. Construction of Judgment Matrix M-C</title><p>The four elements C1, C2, C3, C4 in the criterion layer C are compared two by two to obtain the pairwise comparison matrix; as shown in <xref ref-type="table" rid="table1">Table 1</xref> below.</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> Comparison matrix</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >M</th><th align="center" valign="middle" >C1</th><th align="center" valign="middle" >C2</th><th align="center" valign="middle" >C3</th><th align="center" valign="middle" >C4</th></tr></thead><tr><td align="center" valign="middle" >C1</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.2500</td><td align="center" valign="middle" >0.2500</td></tr><tr><td align="center" valign="middle" >C2</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.2500</td><td align="center" valign="middle" >0.2500</td></tr><tr><td align="center" valign="middle" >C3</td><td align="center" valign="middle" >4.0000</td><td align="center" valign="middle" >4.0000</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >1.0000</td></tr><tr><td align="center" valign="middle" >C4</td><td align="center" valign="middle" >4.0000</td><td align="center" valign="middle" >4.0000</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >1.0000</td></tr></tbody></table></table-wrap><p>If the positive reciprocal inverse matrix satisfies a i j &#215; a j k = a i k , then we call it a consistent matrix.</p><p>Consistency test: 1) Calculate the consistency index CI: CI = λ max − n n − 1 .</p><p>2) Find the corresponding average random consistency index RI ; as shown in <xref ref-type="table" rid="table2">Table 2</xref> below.</p><p>3) Calculate the consistency ratio CR: CR = CI RI . If CR &lt; 0.1, the consistency of the judgment matrix can be considered acceptable, otherwise, the judgment matrix needs to be revised.</p><p>Solving for the eigenvalues of M-C and solving for λ<sub>max</sub> = 4.0000 calculated CR = 0 &lt; 0.1, which passed the consistency test.</p></sec><sec id="s2_3_2"><title>2.3.2. Construction of Judgment Matrices C1-P, C2-P, C3-P, C4-P [<xref ref-type="bibr" rid="scirp.122148-ref10">10</xref>]; As Shown in Tables 3-6 below</title><p>λ<sub>max</sub> = 4.0006, CR<sub>1</sub> = 0.0002 &lt; 0.1, CR<sub>2,3,4</sub> = 0.0000 &lt; 0.1, by calculation, which passed the consistency test [<xref ref-type="bibr" rid="scirp.122148-ref11">11</xref>].</p><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> Relationship between n and RI</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >n</th><th align="center" valign="middle" >2</th><th align="center" valign="middle" >3</th><th align="center" valign="middle" >4</th><th align="center" valign="middle" >5</th><th align="center" valign="middle" >6</th><th align="center" valign="middle" >7</th><th align="center" valign="middle" >8</th><th align="center" valign="middle" >9</th><th align="center" valign="middle" >10</th></tr></thead><tr><td align="center" valign="middle" >RI</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.52</td><td align="center" valign="middle" >0.89</td><td align="center" valign="middle" >1.12</td><td align="center" valign="middle" >1.26</td><td align="center" valign="middle" >1.36</td><td align="center" valign="middle" >1.41</td><td align="center" valign="middle" >1.46</td><td align="center" valign="middle" >1.49</td></tr></tbody></table></table-wrap><table-wrap id="table3" ><label><xref ref-type="table" rid="table3">Table 3</xref></label><caption><title> C1-P judgment matrix</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Population</th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Pakistan</th></tr></thead><tr><td align="center" valign="middle" >United States</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.2266</td><td align="center" valign="middle" >0.2315</td><td align="center" valign="middle" >1.2247</td></tr><tr><td align="center" valign="middle" >India</td><td align="center" valign="middle" >4.4138</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.9591</td><td align="center" valign="middle" >6.7431</td></tr><tr><td align="center" valign="middle" >China</td><td align="center" valign="middle" >4.3205</td><td align="center" valign="middle" >1.0426</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >7.0323</td></tr><tr><td align="center" valign="middle" >Pakistan</td><td align="center" valign="middle" >0.6145</td><td align="center" valign="middle" >0.1483</td><td align="center" valign="middle" >0.1422</td><td align="center" valign="middle" >1.0000</td></tr></tbody></table></table-wrap><table-wrap id="table4" ><label><xref ref-type="table" rid="table4">Table 4</xref></label><caption><title> C2-P judgment matrix</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >GDP</th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Bakkies</th></tr></thead><tr><td align="center" valign="middle" >United States</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >7.4350</td><td align="center" valign="middle" >1.3000</td><td align="center" valign="middle" >8.4317</td></tr><tr><td align="center" valign="middle" >India</td><td align="center" valign="middle" >0.1345</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.1749</td><td align="center" valign="middle" >1.1341</td></tr><tr><td align="center" valign="middle" >China</td><td align="center" valign="middle" >0.7691</td><td align="center" valign="middle" >5.7182</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >6.4851</td></tr><tr><td align="center" valign="middle" >Pakistan</td><td align="center" valign="middle" >0.1186</td><td align="center" valign="middle" >0.8818</td><td align="center" valign="middle" >0.1542</td><td align="center" valign="middle" >1.0000</td></tr></tbody></table></table-wrap><table-wrap id="table5" ><label><xref ref-type="table" rid="table5">Table 5</xref></label><caption><title> C3-P judgment matrix</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Land Area</th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Pakistan</th></tr></thead><tr><td align="center" valign="middle" >United States</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >2.8482</td><td align="center" valign="middle" >0.9753</td><td align="center" valign="middle" >9.3245</td></tr><tr><td align="center" valign="middle" >India</td><td align="center" valign="middle" >0.3511</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.3413</td><td align="center" valign="middle" >3.2755</td></tr><tr><td align="center" valign="middle" >China</td><td align="center" valign="middle" >1.0253</td><td align="center" valign="middle" >2.9303</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >9.5643</td></tr><tr><td align="center" valign="middle" >Pakistan</td><td align="center" valign="middle" >0.1072</td><td align="center" valign="middle" >0.3053</td><td align="center" valign="middle" >0.1045</td><td align="center" valign="middle" >1.0000</td></tr></tbody></table></table-wrap><table-wrap id="table6" ><label><xref ref-type="table" rid="table6">Table 6</xref></label><caption><title> C4-P judgment matrix</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Military Power</th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Pakistan</th></tr></thead><tr><td align="center" valign="middle" >United States</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.4627</td><td align="center" valign="middle" >0.8865</td><td align="center" valign="middle" >0.2882</td></tr><tr><td align="center" valign="middle" >India</td><td align="center" valign="middle" >2.1611</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >1.9157</td><td align="center" valign="middle" >0.6227</td></tr><tr><td align="center" valign="middle" >China</td><td align="center" valign="middle" >1.1280</td><td align="center" valign="middle" >0.5220</td><td align="center" valign="middle" >1.0000</td><td align="center" valign="middle" >0.3251</td></tr><tr><td align="center" valign="middle" >Pakistan</td><td align="center" valign="middle" >3.4702</td><td align="center" valign="middle" >1.6058</td><td align="center" valign="middle" >3.0764</td><td align="center" valign="middle" >1.0000</td></tr></tbody></table></table-wrap></sec><sec id="s2_3_3"><title>2.3.3. Calculate Weights</title><p>To ensure the robustness of the results, we used the arithmetic mean, geometric mean, and eigenvalue methods to find the weights separately, and then calculated the average value, and then calculated the scores of each scheme based on the obtained weight matrix, which avoids the bias arising from using a single method and the conclusions drawn will be more comprehensive and valid [<xref ref-type="bibr" rid="scirp.122148-ref12">12</xref>]. w k is the weight share of each influencing factor in each country.</p><p>Normalization process: find in the four judgment matrices:</p><p>w k = a i j ∑ i = 1 4 a i j   ( k , i , j = 1 , 2 , 3 , 4 ) (1)</p><p>n-dimensional matrix:</p><p>A = [ a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋮ ⋱ ⋮ a n 1 a n 2 ⋯ a n n ] (2)</p><p>Arithmetic averaging:</p><p>ω i = 1 n ∑ j = 1 n a i j ∑ k = 1 n a k j ( i = 1 , 2 , ⋯ , n ) (3)</p><p>Geometric averaging</p><p>ω i = ( ∏ j = 1 n a i j ) 1 n ∑ k = 1 n ( ∏ j = 1 n a k j ) 1 n ( i = 1 , 2 , ⋯ , n ) (4)</p><p>Eigenvalue method: Following the method of consistent matrix weights, we find the maximum eigenvalue of matrix A and the corresponding eigenvector and normalize the found eigenvector to get our weights [<xref ref-type="bibr" rid="scirp.122148-ref13">13</xref>]; as shown in Tables 7-10 below.</p></sec><sec id="s2_3_4"><title>2.3.4. Testing of the Model</title><p>Calculate the country’s score based on the table above, using the United States as an example: 0.1 &#215; 0.0947 + 0.4 &#215; 0.4945 + 0.1 &#215; 0.40254 − 0.4 &#215; 0.12889 = 0.1960. In this indicator of military power is the opposite, the higher the value, the worse the military power, so we take the subtraction to indicate the impact of military power on the calculation of the overall national power, therefore, the United States 0.1684, India −0.0286, China 0.1597, Pakistan −0.1368. This is consistent with the actual situation, which can prove the validity of the model [<xref ref-type="bibr" rid="scirp.122148-ref14">14</xref>].</p><table-wrap id="table7" ><label><xref ref-type="table" rid="table7">Table 7</xref></label><caption><title> Arithmetic average method of calculating weights</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Pakistan</th><th align="center" valign="middle" ></th></tr></thead><tr><td align="center" valign="middle" >Population</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.0965</td><td align="center" valign="middle" >0.4182</td><td align="center" valign="middle" >0.4271</td><td align="center" valign="middle" >0.0611</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >GDP</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.4945</td><td align="center" valign="middle" >0.0665</td><td align="center" valign="middle" >0.3803</td><td align="center" valign="middle" >0.1210</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >Land Area</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.4025</td><td align="center" valign="middle" >0.1412</td><td align="center" valign="middle" >0.4131</td><td align="center" valign="middle" >0.0427</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >Military Power</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.1289</td><td align="center" valign="middle" >0.2785</td><td align="center" valign="middle" >0.1454</td><td align="center" valign="middle" >0.4472</td><td align="center" valign="middle" >1</td></tr></tbody></table></table-wrap><table-wrap id="table8" ><label><xref ref-type="table" rid="table8">Table 8</xref></label><caption><title> Geometric averaging method to calculate weights</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Pakistan</th><th align="center" valign="middle" ></th></tr></thead><tr><td align="center" valign="middle" >Population</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.0911</td><td align="center" valign="middle" >0.4183</td><td align="center" valign="middle" >0.4294</td><td align="center" valign="middle" >0.0610</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >GDP</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.4944</td><td align="center" valign="middle" >0.0665</td><td align="center" valign="middle" >0.3803</td><td align="center" valign="middle" >0.0586</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >Land Area</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.4025</td><td align="center" valign="middle" >0.1412</td><td align="center" valign="middle" >0.4131</td><td align="center" valign="middle" >0.0431</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >Military Power</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.1288</td><td align="center" valign="middle" >0.2785</td><td align="center" valign="middle" >0.1453</td><td align="center" valign="middle" >0.4472</td><td align="center" valign="middle" >1</td></tr></tbody></table></table-wrap><table-wrap id="table9" ><label><xref ref-type="table" rid="table9">Table 9</xref></label><caption><title> Eigenvalue method for calculating weights</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Pakistan</th><th align="center" valign="middle" ></th></tr></thead><tr><td align="center" valign="middle" >Population</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.0966</td><td align="center" valign="middle" >0.4265</td><td align="center" valign="middle" >0.4175</td><td align="center" valign="middle" >0.0594</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >GDP</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.4945</td><td align="center" valign="middle" >0.0665</td><td align="center" valign="middle" >0.3803</td><td align="center" valign="middle" >0.0587</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >Land Area</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.4026</td><td align="center" valign="middle" >0.1414</td><td align="center" valign="middle" >0.4128</td><td align="center" valign="middle" >0.0432</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >Military Power</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.1289</td><td align="center" valign="middle" >0.2785</td><td align="center" valign="middle" >0.1454</td><td align="center" valign="middle" >0.4472</td><td align="center" valign="middle" >1</td></tr></tbody></table></table-wrap><table-wrap id="table10" ><label><xref ref-type="table" rid="table1">Table 1</xref>0</label><caption><title> Indicator weighting table</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th><th align="center" valign="middle" >United States</th><th align="center" valign="middle" >India</th><th align="center" valign="middle" >China</th><th align="center" valign="middle" >Pakistan</th></tr></thead><tr><td align="center" valign="middle" >Population</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.0947</td><td align="center" valign="middle" >0.4210</td><td align="center" valign="middle" >0.4247</td><td align="center" valign="middle" >0.0605</td></tr><tr><td align="center" valign="middle" >GDP</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0.4945</td><td align="center" valign="middle" >0.0665</td><td align="center" valign="middle" >0.3803</td><td align="center" valign="middle" >0.0794</td></tr><tr><td align="center" valign="middle" >Land Area</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.4025</td><td align="center" valign="middle" >0.1413</td><td align="center" valign="middle" >0.4130</td><td align="center" valign="middle" >0.0430</td></tr><tr><td align="center" valign="middle" >Military Power</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >0.1288</td><td align="center" valign="middle" >0.2785</td><td align="center" valign="middle" >0.1453</td><td align="center" valign="middle" >0.4472</td></tr></tbody></table></table-wrap><p>Ebraic regression system is y = a<sub>0</sub> + a<sub>1</sub>x<sub>1</sub> + a<sub>2</sub>x<sub>2</sub> + a<sub>3</sub>x<sub>3</sub> + a<sub>4</sub>x<sub>4</sub> + b, where y is the explanatory variable, i.e., the dependent variable; x<sub>1</sub>-x<sub>4</sub> is the explanatory variable, i.e., the independent variable; a<sub>0</sub> is the regression constant; a<sub>1</sub>-a<sub>2</sub> is the regression coefficient; and b is the random error [<xref ref-type="bibr" rid="scirp.122148-ref15">15</xref>].</p></sec></sec></sec><sec id="s3"><title>3. Conclusion</title><p>In this paper, we define global equity and develop a global equity model using hierarchical analysis. And we verified the validity of the model. We hope that when asteroid mining becomes a reality, the problem of resource allocation can be properly dealt with, and the fairness between countries and people can be truly achieved.</p></sec><sec id="s4"><title>Conflicts of Interest</title><p>The author declares no conflicts of interest regarding the publication of this paper.</p></sec><sec id="s5"><title>Cite this paper</title><p>Qian, S.Y. (2022) A Mathematical Model of Global Equity for Allocating Asteroid Resources Based on Analytic Hierarchy Process. 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