Lost In Nature Torrent Download 'LINK' [Password]

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Finding a fair game in the N-person simple majority game

The N-person simple majority game is played on an $N$-person game board with each player choosing either "yes" or "no". This game is played as follows: at each stage of the game all players vote with their "yes" or "no" once and whoever has the majority wins. Let $N = n + 3$ where $n \in \mathbb N$ and suppose $n\geq2$. My question is, how would you find a fair game in this simple majority game?

A:

Let $S_k(n,\alpha)$ denote the set of all games in which no fewer than $\alpha$ players say "yes" in a round in which exactly $k$ say "yes." Then the set of all fair games is the intersection of the sets $S_k(n,\alpha)$ where $k \in [n]$ and $\alpha \in \{0,n-3\}$, namely
$$\bigcap_{k=0}^n \bigcap_{\alpha=0}^{n-3} S_k(n,\alpha).$$
This describes a very simple and intuitively obvious fact; it's about as much work as it would take to write out a terse mathematical proof, and I doubt there's any general mathematical proof of this fact.
Most of the sets $S_k(n,\alpha)$ are easy to describe; I encourage you to find them in a moment. The hardest case is $S_n(n,n-3)$, which involves a sum of $n$ geometric series whose ratios are $r_i = \frac{1}{1+\frac{i-1}{n}}$. These are pretty difficult to compute, but their sum simplifies to $r = \frac{n+1

https://colab.research.google.com/drive/1jz5M5tJtdMWkExFiyE7LcOvacU_mqRZL
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https://colab.research.google.com/drive/15RnaxFF-oHmMvVS2e6TAv8bP-IjxoWJA

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2017 NATURE. Lost to be different. What does nature do to create diversity.New MTV series premieres tonight

The first episode of the spin-off to Jersey Shore, called Shore-Up, features LA chef Dario DeBitetto, a self-professed Shore-Up devotee who claims he'll be the best food critic there is -- except he's always got his fair share of drama.

The LA Times is reporting that MTV's have given it the green light for an initial 15-episode run.

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Video: Shore-Up Promo

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Rise of Facebook's Passive Service Ambitions - jacquesm

======
rdegges
OK, I'll go ahead and say it, I think that Facebook has no intention of
implementing a closed platform, and would likely never do so, given the risk
of backlash.

Instead, Facebook _has_ been working on many of these ideas for the past 3-4
years (e.g. Spaces, Currents, Oculus, etc.) and basically has built it's
entire infrastructure around them. The reason these are essentially invisible
to the average user is because they're not trying to replace Facebook with
something. Instead, they're trying to augment the platform - making it better
in various ways, and letting you do all your social interaction elsewhere.

Yes, it's entirely possible Facebook will try to sue developers for using
these platforms. Yes, it might be seen as evil by some. But the reality is
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