Choose the sentence or sentences that accurately restate Arrow's Impossibility Theorem.
1. It is mathematically impossible for any democratic voting system to satisfy any of the four fairness criteria.
II. It is mathematically impossible for any democratic voting system to satisfy all of the four faimess criteria.
III. It is mathematically impossible for any democratic voting system to satisfy some of the four fairness criteria. IV. It is mathematically impossible for any democratic voting system to satisfy any more than one of the four fairness criteria.
1.11. and III
1,111 , and iv
II only
W only
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Step 1 ：Arrow's Impossibility Theorem states that no rank-order electoral system can be designed that always satisfies these three 'fairness' criteria: 1. If every voter prefers alternative X over alternative Y, then the group prefers X over Y. 2. If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change). 3. There is no 'dictator': no single voter possesses the power to always determine the group's preference.

Step 2 ：From the given options, the sentence that accurately restates Arrow's Impossibility Theorem is 'It is mathematically impossible for any democratic voting system to satisfy all of the four fairness criteria.'

Step 3 ：However, it's important to note that Arrow's theorem actually involves three criteria, not four. The question might have a typo or the fourth criterion might be an additional one not included in the original theorem.

Step 4 ：Final Answer: \(\boxed{\text{II only}}\)