Switching is not same as joining

Post #197,232 by Arkadiy 3/4/05 3:37:26 PM Reply	Switching is not same as joining 60% gain may not justify the switch if it's costly for the user. In any case, there has to be a reason for _the_particular_user_ to switch. We're entering into micro-level here, and formulae do not apply. However, when I consider joining a new network, the one larger by 30% wins hands down, all other things being equal. -- And what are we doing when the two most powerful nations on earth -- America and Israel -- stomp on the elementary rights of human beings? -- letter to the editor from W. Ostermeier, Liechtenstein
Post #197,438 by ben_tilly 3/7/05 4:21:04 AM Reply	Larger by 30% wins? Suppose that you're comparing company A, much smaller but has very good penetration in your area, with company B, new to your area but much larger (their home base is, say, Japan). Which do you prefer? Odds are that you prefer A, because most of the people that you care about are going to be on that network. Despite company B having more people, you're not going to experience more value there. If you think carefully about that hypothetical, the heart of our criticism of Metcalfe's law is right there. Incidentally I think that the following paragraph is key: Metcalfe's Law is intuitively appealing, since our personal estimate of the size of a network is based on uptake of that network among friends and family. Our derived value also varies directly with the metric. We therefore see a linear relationship between the perceived size and value of that network. Of course this intuition leads us astray because we do not percieve the vast majority of the network, and therefore have bad intuition of what its true size is. Cheers, Ben I have come to believe that idealism without discipline is a quick road to disaster, while discipline without idealism is pointless. -- Aaron Ward (my brother)
Post #197,458 by Arkadiy 3/7/05 9:26:01 AM Reply	I guess I should re-read I have to agree with you that when we say "size of network" we mean, most of the time, "number of people I want to connect to on network". But that would simply lead to change of "n" in "n^2". I'll have to re-read for comprehension :) and figure out how you get from the "the heart of our criticism" to n log n. -- And what are we doing when the two most powerful nations on earth -- America and Israel -- stomp on the elementary rights of human beings? -- letter to the editor from W. Ostermeier, Liechtenstein
Post #197,475 by ben_tilly 3/7/05 11:23:39 AM Reply	Read section 4 We present several arguments suggesting n log(n). The one that you want is in section 4. Zipf's law says that the value of the n'th thing tends to be 1/n times the value of the first. This has been found to apply in a wide range of different areas. (Personal wealth, size of cities, etc.) If this holds for the potential value of connections over networks, and the value of the most important connections is fixed by the medium and human nature, then the average value from being in a network is the value of the most valuable times (1 + 1/2 + ... + 1/n) which scales as log(n). Over n people this totals n log(n). Cheers, Ben I have come to believe that idealism without discipline is a quick road to disaster, while discipline without idealism is pointless. -- Aaron Ward (my brother)
Post #197,487 by drewk 3/7/05 12:26:30 PM 3/7/05 12:26:44 PM Reply	There's your example :-) Odds are that you prefer A, because most of the people that you care about are going to be on that network. You asked for an example where the smaller network was more valuable. There it is. === Purveyor of Doc Hope's [link\|http://DocHope.com\|fresh-baked dog biscuits and pet treats]. [link\|http://DocHope.com\|http://DocHope.com] Edited by drewk March 7, 2005, 12:26:44 PM EST Expand All History
Post #197,493 by ben_tilly 3/7/05 12:57:30 PM Reply	More valuable to you, yes More valuable across all members of the network? No. Cheers, Ben I have come to believe that idealism without discipline is a quick road to disaster, while discipline without idealism is pointless. -- Aaron Ward (my brother)

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